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Geometry Semester 2 Final Practice ProblemsMultiple ChoiceIdentify the choice that best completes the statement or answers the question.1.Classify the triangle according to its sides and angles.a.scalene; acutec.isosceles; obtuseb.equilateral; obtused.equilateral; acute2.Classify the triangle according to its sides and angles.a.isosceles; rightc.equilateral; acuteb.equilateral; rightd.isosceles; acute3.Classify the triangle according to its sides and angles.a.isosceles; obtusec.scalene; obtuseb.scalene; rightd.isosceles; right4.Tell whether the slope of the line is positive or negative. Then, determine the slope.a.positive; c.negative; b.negative; d.negative; 5.Write the converse of the statement, “If a dog is a bloodhound, then it has floppy ears.”a.If a dog has floppy ears, then it is a bloodhound.b.If a dog is not a bloodhound, then it does not have floppy ears.c.If a dog does not have floppy ears, then it is not a bloodhound.d.If a dog has floppy ears, then it is not a bloodhound.6.Write the inverse of the statement, “If a figure is a square, then it has four sides.”a.If a figure does not have four sides, then it is not a square.b.If a figure is not a square, then it does not have four sides.c.If a figure has four sides, then it is not a square.d.If a figure has four sides, then it is a square.7.Write the contrapositive of the statement, “If a state's capital is Denver, then the state is Colorado.”a.If a state is Colorado, then its capital is not Denver.b.If a state is Colorado, then its capital is Denver.c.If a state is not Colorado, then its capital is not Denver.d.If a state's capital is not Denver, then the state is not Colorado.8.What is the equation of a line that has slope and passes through (–4,?–5)?a.c.b.d.9.Determine the slope of the line containing points (6,?9) and (4,?3).a.c.b.d.10.Given a conditional statement of the form “If x, then y”, what form is its contrapositive?a.If ~x, then ~y.d.If y, then x.b.If ~y, then ~x.e.None correctc.If y, then ~x.11.What is the interior angle measure of a regular pentagon?a.45°c.108°b.180°d.540°12.Find the measure of each exterior angle for a regular pentagon.a.108°c.180°b.540°d.72°13.What is the sum of the interior angle measures of a convex, irregular hexagon?a.540°d.720°b.1080°e.None correctc.1440°14.Find the area of a trapezoid with parallel sides measuring 5 feet and 10 feet and a height of 3 feet.a.7.5 c.75 b.150 d.22.5 15.In , , , and . In , , , and . Write the congruency statement for the triangles.a.c.b.d.16.A major arc has a measure of . Its corresponding minor arc has a measure of . Find x.a.110c.200b.34d.7017.An arc of a circle has an arc measure of 82 degrees. If the circle has a radius of 11.4 units, what is the length of the arc? Round to the nearest hundredth.a.55.31d.32.63b.110.63e.None correctc.16.3218.Find the area of the parallelogram.a.18.5 cm2c.71.5 cm2b.37 cm2d.143 cm219.Find the area of the trapezoid.a.720 in.2c.240 in.2b.180 in.2d.18 in.220.Find the circumference of the circle to the nearest tenth. Use 3.14 for ?.a.907.5 in.c.2849.4 in.b.53.4 in.d.106.8 in.21.Find the circumference and area of the circle to the nearest tenth. Use 3.14 for .a. cm; cm 2c. cm; cm 2b. cm; cm 2d. cm; cm 222.Emi is making a circular garden and needs to know how much edging material she needs to go around it. If the diameter of the garden is 49 feet, what is its circumference? Use for ?.a. ftc. ftb. ftd. ft23.What is ?a.75c.255b.15d.10524.What is m?a.m = c.m = b.m = d.m = 25.Find the sum of the interior angle measures by dividing the polygon into triangles. If necessary, round your answer to the nearest hundredth.a.1080°c.1440°b.45°d.135°26.Find the measure of each interior angle of a regular 40-gon.a.189c.171b.175.5d.16227.Find the measure of each exterior angle of a regular pentagon.a.60°c.36°b.72°d.120°28.The door on a spacecraft is formed with 6 panels that overlap to form a regular hexagon. What is the measure of ?a.m = 60oc.m = 720ob.m = 120od.m = 45o29.MNOP is a parallelogram. Find MP.a.MP = 25c.MP = 20b.MP = 30d.MP = 630.The diagram shows the parallelogram-shaped component that attaches a car’s rearview mirror to the car. In parallelogram RSTU, UR = 25, RX = 16, and = 42.4o. Find ST, XT, and mRST.a.ST = 16, mRST = 42.4, XT = 25c.ST = 25, mRST = 137.6, XT = 16b.ST = 25, mRST = 47.8, XT = 16d.ST = 5, mRST = 137.6, XT = 431.Find the length of arc with measure 100° in a circle with radius 2 in. Round to the nearest tenth.a.c.b.d.32.Find the area of sector POM. Give your answer in terms of .a.c.b.0d.33.Determine if you can use the Leg-Angle Congruence Theorem to prove . Explain.a.. However, no angles are known to be congruent, so LA cannot be applied.b. and are hypotenuses, not legs, so LA cannot be applied. You would need to use HA to prove that .c.. because both are right angles. Therefore, by LA.d.. because vertical angles are congruent. Therefore, by LA.34.For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.a., HLc., SASb., HLd., SAS35.For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.a., HLc., LLb., LLd., HL36.The equations of four lines are given. Identify the parallel lines..Line 1:y = x + 5Line 2:x + y = –8Line 3:y = x + 6Line 4:y – 2 = (x – 8)a.Lines 1 and 2 are parallel.b.All four lines are parallel.c.Lines 1 and 4 are parallel.d.Lines 2 and 3 are parallel.37.The equations of four lines are given. Identify the perpendicular lines.Line 1: Line 2: Line 3: Line 4: a.Lines 1 and 3 are perpendicular; Lines 2 and 4 are perpendicular.b.Lines 1 and 3 are perpendicular.c.None of the lines are perpendicular.d.Lines 2 and 4 are perpendicular.38.Write an equation in slope-intercept form for the line parallel to y = x – 7 that passes through the point (–2, –7).a.y = x + c.y = x – b.y = x – 7d.y = x – 39.In parallelogram QRST, if measures 44°, what is the measure of ?a.22°c.136°b.44°d.46°40.Which congruence theorem applies to these triangles?a.HL Congruence Theoremc.LA Congruence Theoremb.HA Congruence Theoremd.LL Congruence Theorem41.What is the equation of a line that is perpendicular to and passes through (0,?–2)?a.c.b.d.42.Find a line that is parallel to and passes through point (4,?1).a.c.b.d.43.Which line is parallel to ?a.d.b.e.None correctc.44.Given the following similar triangles, find the length of .a.7c.6b.2d.2445.Given , , with , , and , , what is the ratio of their corresponding sides?a.8 : 4d.7 : 1b.4 : 1e.None correctc.7 : 446.Find the distance from the center of a circle to a 6-inch chord if the circle has a 16-inch diameter. Round your answer to the nearest hundredth if necessary.a.7.42 inchesc.8 inchesb.8.54 inchesd.3 inches47.A circle has diameter of 12 inches, and a chord is 6 inches long. What is the distance in inches from the chord to the center of the circle, to the nearest hundredth?a.5.20d.27.00b.3.00e.None correctc.10.3948.ABCD and EFGH are similar polygons. Their corresponding sides have a ratio of 2:3. If the perimeter of ABCD is 36 inches, what is the perimeter of EFGH?a.72 inchesc.108 inchesb.54 inchesd.24 inches49.What is the measure of the inscribed angle if its intercepted arc measure 92°?a.184°c.92°b.46°d.88°50.Classify the three-dimensional solid shown below.a.pyramidc.sphereb.rectangular prismd.cylinder51. . Find XY. a.s = 16.6c.s = 15b.s = 41.67d.s = 10.5852.Find the distance from P(–1, 2) to the line x = –4.a.6c.7b.4d.353.Find .a. = 16c. = 5b. = 8d. = 1054.The front of Jane’s house is similar in shape to the front of Spot’s doghouse. The base of the doghouse is 3 feet and the height is 3.5 feet. If the height of Jane’s house is 28 feet, what is the length of its base? If necessary, round your answer to the nearest tenth.a.32.7 ftc.27.5 ftb.10.5 ftd.24 ft55.The plans for a new community include a rectangular park that has a perimeter of 600 ft. Dionne creates a model so that the similarity ratio of the model to the park is . What is the perimeter of the model in inches?a.300,000 in.c.1 in.b.14.4 in.d.7,200 in.56.Explain why and then find BC.a. by the Converse of the Corresponding Angles Postulate. by the Corresponding Angles Postulate. by AA Similarity.Corresponding sides are proportional, so .b. by the Converse of the Alternate Interior Angles Theorem. by the Alternate Interior Angles Theorem. by AA Similarity.Corresponding sides are proportional, so .c. by the Reflexive Property of Congruence. by AA Similarity.Corresponding sides are proportional, so .d., by the Corresponding Angles Postulate. by AA Similarity.Corresponding sides are proportional, so .57.Verify that .a. by the Reflexive Property of Congruence. by SAS Similarity.b. and by the Corresponding Angles Postulate. by AA Similarity.c. and by the Alternate Interior Angles Theorem. by AA Similarity.d. by the Reflexive Property of Congruence. by SAS Similarity.58.Find .a. = 9?c. = 18?b. = 46?d. = 36?59.A wheel from a motor has springs arranged as in the figure. Find m.a.m = c.m = b.m = d.m = 60.Identify the bases and faces of the polyhedron. Then classify the polyhedron.a.bases: 2 hexagonal prismsfaces: 6 rectanglesname: hexagonc.bases: 6 hexagonsfaces: 6 rectanglesname: hexagonal prismb.bases: 2 hexagonsfaces: 6 rectanglesname: hexagonal prismd.bases: 1 hexagonfaces: 6 rectanglesname: hexagonal pyramid61.Write a similarity statement comparing the three triangles in the diagram.a.c.b.d.62.Find x, y, and z. Express your answers in radical form.a.x = 5, y = , z = c.x = 3, y = 4, z = b.x = 2.5, y = , z = d.x = , y = , z = 63.Find the geometric probability of the spinner landing on an even number. a.40%d.30%b.20%e.None correctc.50%64.Triangle ABC is isosceles and its vertex angle is at B. If , find .a.122°c.64°b.32°d.29°65.The diagonals of rectangle ABCD intersect at point E. if AE is 11 inches long, what is the length of ?a.11 inchesc.44 inchesb.5.5 inchesd.22 inches66.In the diagram, is a midsegment of . Find the value of x.a.16.5c.27.5b.22d.3367.A tree’s shadow is 6 feet long, and the sun is at an angle of elevation of 60° above the horizon. What is the height of the tree? Give your answer in simplified radical form.a.d.b.e.None correctc.68.A right, rectangular prism has a length, width, and height that are all equal. The volume of the prism is 1331 cubic meters. Find the surface area of this prism. a.968 c.484 b.726?d.363 69.Find the value of y.a.21c.42b.49d.2770.Solve for h in the isosceles triangle.a.h = 11.7°c.h = 69°b.h = 19°d.h = 119°71.An artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center of the quilt. The dimensions of the rectangle are inches and inches. Find .a. = 7 inchesc. = 5 inchesb. = 10 inchesd. = 14 inches72.Find the value of x. Express your answer in simplest radical form.a.x = c.x = b.x = d.x = 73.Given with , , and , find the length of midsegment .a.XY = 3c.XY = 2.5b.XY = 1.5d.XY = 274.Find the values of x and y. Express your answers in simplest radical form.a., c., b., d., 75.Find the perimeter of . If necessary, round your answer to the nearest tenth of a centimeter.a.30.3 cmc.22.9 cmb.41.4 cmd.21.8 cm76.Find the lateral area and surface area of a regular triangular right prism with base edge 8 cm and height 13 cm. Round to the nearest tenth.a.lateral area: ;surface area: c.lateral area: ;surface area: b.lateral area: ;surface area: d.lateral area: ;surface area: 77.Find the volume of a right rectangular prism with length 13 in., width 10 in., and height 6 in. Round to the nearest tenth, if necessary.a.780 in3c.260 in2b.2,600 in3d.390 in378.Find the volume of the triangular prism.a.560 ft3c.460 ft3b.34 ft3d.280 ft379.Find .a. = 1c. = 1.6b. = 1.25d. = 280.Find the probability of the spinner landing on “new house”. Give your answer as a fraction.a.c.b.60d.81.A point is chosen randomly on . Find the probability that the point is not on .a.c.6b.3d.82.If a can is 20 inches tall and has a radius of 8 inches, how many cubic inches of water can the can hold?a.c.b.d.83.For an art project, Ana needs to spray paint a soup can on all sides, including the bases. The can is 5 inches tall and it has a radius of 3 inches. Find the area to be painted to the nearest square inch.a.d.b.e.None correctc.84.What is , given that is a tangent?a.72°d.144°b.54°e.108°c.None correct85.In trapezoid MNOP, legs and are congruent. If , find .a.52°c.26°b.128°d.138°86.A rectangular pyramid has a base area of 46 square feet and a height of 6 feet. What is the volume of the pyramid?a.138 c.828 b.276 d.92 87.Find the lateral area and surface area of the cylinder. Give your answers in terms of .a.lateral area: ;surface area: c.lateral area: ;surface area: b.lateral area: ;surface area: d.lateral area: ;surface area: 88.Find the volume of the cylinder. Use 3.14 for ?. Round your answer to the nearest tenth.a.409.8 m3c.1,639.1 m3b.136.6 m3d.1,980.6 m389. is tangent to the circle at A. Find m. a.m = 130°c.m = 65°b.m = 115°d.m = 45°90.Identify the following as a translation, rotation, reflection, or none of these.a.None of thesec.Reflectionb.Translationd.Rotation91.Give the sine, cosine, and tangent of .a. ; ; c. ; ; b. ; ; d. ; ; 92.Use a calculator to evaluate sin 23, cos 49, and tan 58. Round to the nearest hundredth.a.sin 23= 0.66, cos 49 = 0.39, tan 58 = 1.6b.sin 23 = 0.3, cos 49 = –0.85, tan 58 = 8.33c.sin 23 = –0.85, cos 49 = 0.3, tan 58 = 8.33d.sin 23 = 0.39, cos 49 = 0.66, tan 58 = 1.693.Vinay is building a ramp for loading furniture onto a truck. The trailer is 2.8 feet off of the ground. To avoid making it too difficult to roll furniture up the ramp, he decides to make the angle between the ramp and the ground 15. Find the length of the ramp r to the nearest hundredth of a foot.a.10.82 feetc.0.72 feetb.2.90 feetd.10.45 feet94.Find the lateral area and surface area of a square pyramid with base edge length 5 m and slant height 9 m.a.lateral area: ;surface area: c.lateral area: ;surface area: b.lateral area: ;surface area: d.lateral area: ;surface area: 95.Find the volume of the rectangular pyramid. Round your answer to the nearest tenth.a.4.7 cm3c.84 cm3b.14 cm3d.28 cm396.Draw the image of a triangle with vertices (1, 3), (2, 5), and (4, 3). Then perform the following transformation: translate 6 units down .a.c.b.d.97.Translate the triangle with vertices along the vector . Find the coordinates of the new image.a.c.b.d.98.A tree casts a shadow of 26 meters when the angle of elevation of the sun is 30°. Find the height of the tree to the nearest meter.a.23 mc.15 mb.338 md.17 m99.An eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15. What is the horizontal distance between the eagle and its prey? Round to the nearest foot.a.1,120 ftc.310 ftb.1,159 ftd.723 ft100.A pilot flying at an altitude of 1.8 km sights the runway directly in front of her. The angle of depression to the beginning of the runway is 31. The angle of depression to the end of the runway is 23?. What is the length of the runway? Round to the nearest tenth of a kilometer.a.1.2 kmc.1.3 kmb.0.9 kmd.1.0 km101.A surveyor whose eye level is 5 feet above the ground determines the angle of elevation to the top of an office building to be 41.7°. If the surveyor is standing 40 feet from the base of the building, what is the height of the building to the nearest foot?a.41 ftc.32 ftb.50 ftd.36 ft102.Write the equation of a circle with center M(–8, – 2) and radius 4.a.c.b.d.103.Graph the equation .a.c.b.d.104.An ice cream cone has a diameter of 10.4 cm and a slant height of 8.8 cm. Find the lateral surface area of the cone. Use 3.14 for ?. Round your answer to the nearest tenth.a.84.9 cm2c.287.4 cm2b.228.6 cm2d.143.7 cm2105.Find the surface area of the cone. Use 3.14 for ?. Round your answer to the nearest tenth.a.559.5 cm2c.422.8 cm2b.136.8 cm2d.57,825.7 cm2106.Find the lateral area and surface area of a right cone with radius 5 in. and height 12 in. Give your answers in terms of .a.lateral area: ;surface area: c.lateral area: ;surface area: b.lateral area: ;surface area: d.lateral area: ;surface area: 107.Find the volume of the cone. Use 3.14 for ?. Round your answer to the nearest tenth.a.1,234.8 ft3c.74.8 ft3b.31.7 ft3d.411.6 ft3108.Find m.a.m = c.m = b.m = d.m = 109.Two of the muscles that control eye movement are attached to the eyeball and intersect behind the eye as shown. If , what is ?a. = c. = b. = d. = 110.Find the surface area of the sphere, both in terms of ? and as a number. Use 3.14 for ?. Round your answers to the nearest tenth.a.309.8? cm2 ? 972.6 cm2c.908.6? cm2 ? 2,853.1 cm2b.77.4? cm2 ? 243.2 cm2d.1,239? cm2 ? 3,890.6 cm2111.Find the volume of a sphere with a diameter of 9.6 cm, both in terms of ? and as a number. Use 3.14 for ?. Round your answers to the nearest tenth.a.147.5? cm3 ? 463 cm3c.82.9? cm3 ? 260.4 cm3b.92.2? cm3 ? 289.4 cm3d.36.9? cm3 ? 115.8 cm3112.Find the surface area of a sphere with volume 166.67 m3. Give your answer in terms of .a.500 m2c.100 m2b.5 m2d.100 m2113.A point is translated 4 units to the right. What are the coordinates of the new image?a.c.b.d.114.If (7,?7) is a point on and the center of is , then which of the following could be an equation for ?a.c.b.d.115.A cone has a radius of 4 inches and a slant height of 12 inches. Calculate the lateral area of the cone using 3.14 for ?.a.50.24 c.150.72 b.602.88 d.301.44 Numeric Response116.An isosceles triangle has a perimeter of 50 in. The congruent sides measure (2x + 3) cm. The length of the third side is 4x cm. What is the value of x?117.A right triangle has a hypotenuse of 65 inches and one leg that measures 60 inches. What is the length of the third side in inches?118.Find the slope of the line below.119.Determine the slope of the line passing through (6,?5) and (5,?–3).120.Amy is painting two murals in her art studio. One is shaped like a trapezoid and the other is shaped like a parallelogram. Use the diagram to find how many square feet Amy will need to paint.121.Find the area, in square feet, of the parallelogram below.122.Find the area, in square inches, of the trapezoid below.123.Find the area of the trapezoid below in square centimeters.124.Find the area, in square feet, of a parallelogram if the height is 9 feet and the base is 4 feet.125.Find the circumference of a circle with a diameter of 12. Use 3.14 for ?.126.Find the circumference of the circle with radius of 2 feet. Use 3.14 for ? and round to the nearest tenth of a foot.127.Find the area, in square inches, of a circle with a radius of 6 inches. Use 3.14 for ?.128.A circle has a diameter of 11 inches. What is the area, in square inches, of the circle to the nearest square inch? Use 3.14 for ?.129.If , find x.130.Find the distance between the point (3,?2) and the line .131.Find the distance, in units, from the point P (–9, –5) to the line x = –4.132.Find the distance from point to the line .133.Find the distance from point to the line .134.Find the distance, in units, from point A(3,?7) to the line x = 9.135.Hexagons ABCDEF and GHIJKL are regular hexagons and are similar to each other. The similarity ratio of ABCDEF to GHIJKL is 3:1. Find the perimeter of GHIJKL if AB=7.136.Figures ABCD and WXYZ are similar polygons. Their corresponding sides have a ratio of . If the perimeter of figure ABCD is 51 inches, what is the perimeter, in inches, of figure WXYZ?137.Suppose a spinner is comprised of three colored sectors: green, yellow, and red with central angles measuring 150°, 72°, and 138° respectively. What is the probability of spinning yellow?138.A triangle is equiangular and has a perimeter of 27 inches. Determine the length of each side in inches.139.A rectangular frame is divided by diagonal edges as shown below. If PI is 17 inches long, what is the length of in inches?140.Find the perimeter of the triangle. Round your answer to the nearest whole number.141.Find the lateral area, in square inches, of the regular triangular prism shown below.142.Find the volume, in cubic feet, of a right prism if the base is a 8-feet-by-6-feet rectangle and the height is 4 feet.143.Find the perimeter of a regular pentagon if one side measures 6.144.In the diagram below, use the tangent function to find a to the nearest hundredth.145.Find the volume, in cubic centimeters, of a tetrahedron, a regular triangular pyramid where all faces are congruent, with a base area of 5.4 square centimeters and a height of 2.95?centimeters.146.In , m = and m = . Find .147.From the ground 28 feet away from a tree, the angle of elevation to the top of the tree is 33°. Find the height of the tree to the nearest foot.148.A person is standing 300 feet away from a building. The angle of elevation from the person to the roof of the building is 49°. Find the height of the building to the nearest foot.149.Calculate the lateral area, in square inches, of a right cone with a radius of 7 inches and a slant height of 17 inches to the nearest hundredth square inch.150.Find the surface area, in square meters, of a hemisphere with a 11-meter diameter. Use 3.14 for ?.151.A spherical globe has a radius of 9 inches. What is the surface area of the globe to the nearest hundredth of a square inch?Problem152.Write the equation of the line that has slope and passes through (–4, –5).153.Consider the conditional statement “” State the hypothesis and conclusion of this statement and write its converse. If the original statement is true, is the converse true?154.Determine the contrapositive of the statement below.155.Write the inverse of the statement below. Is the statement true? Is the inverse of the statement true?156.Write the biconditional of the statement and its converse.If , then .Is it true? Explain why or why not.157.Determine the measure of each exterior angle for a regular triangle.158.What is the sum of the interior angle measures of a convex, irregular pentagon?159.Write a congruence statement for the two triangles below.160.For , , , . For , , , . Write the congruency statement for the triangles.161.Identify a central angle, minor arc, major arc, and semicircle in .162.What is ?163.Find the value of x in the triangle below. Write your answer in simplified radical form.164.Determine whether the triangle below is a right triangle.165.A triangle has side lengths that measure 20, 7, and 14 units. Classify the triangle by side lengths and angles.166.In the parallelogram shown, what are the measures of ?167.Find the arc length L of a circle with a radius of 6 feet and an arc measure of 120°. Give the answer in terms of ?.168.Find the area of sector AOB with radius 12 feet and . Give your answer in terms of ?.169.Find a line that is parallel to y = x + 5 and passes through the point (–5, –4).170.Find a line that is perpendicular to and passes through point .171.Write the equation of a line that is parallel to and passes through point .172.Write the equation of a line that is perpendicular to and passes through the point .173.Consider shown below. Write a proportion to show that .174.Find the unknown side lengths in the two similar triangles below.175.The circle shown has a diameter of 12 inches. Chord is 8 inches long. How far is from the center of the circle?176.The pentagons in the diagram are similar. Find the values of x and y.177.Name the inscribed angle shown in the circle below178.Find the measure of , , and in the diagram below.179.Classify the three-dimensional solid shown below.180.Given the triangle, find the missing values a and b using the relationships created by the altitude. Round your answers to the nearest hundredth if necessary.181.Find AD and AB in the diagram below. 182.A spinner is divided into 6 equal sectors. Sector 1 is colored red, sectors 2–4 are colored blue, and sectors 5–6 are colored yellow. What are the measures of the red, blue, and yellow central angles?183.Triangle ABC is isosceles, and its vertex angle is at B. If , determine and .184.If the vertex angle of an isosceles triangle measures , what are the measures of each of its base angles?185.Find the exact length of a hypotenuse of a 45°-45°-90° right triangle if one leg measures 8 centimeters.186.In the diagram below, is a midsegment of triangle CDE. Find the values of x and y.187.Find the values of x and y. Give your answer in simplified radical form.188.Find the perimeter of the triangle shown below. Give your answer in simplified radical form.189.Line m is tangent to at point T, and line n passes through C, the center of . Lines m and n intersect at point S. Line n contains , a radius of .a. Sketch and lines n and m. Mark C, R, S, and T on your sketch.b. If , determine .c. Explain how you arrived at your answer in part b.d. What is ?e. If inches, find the arc length of . Give your answer in terms of ?.190.Line p is tangent to at A, and line q passes through C. Lines p and q intersect at B. If , determine .191.Find QU.192.Find in the figure below, given that is a tangent.193.Find the measures of , , and in trapezoid PQRS.194.Ron is building a silo with the measurements shown.a.Find the surface area of the silo, excluding the floor, to the nearest whole meter. Use 3.14 for ?. Show your work.b.Find the volume of the silo to the nearest whole meter. Use 3.14 for ?. Show your work.195.In the diagram below, if B is a point on , write the equation of .196.The equation of is . Graph .197.Write an equation to relate all the x- and y-coordinates of points that lie on with a radius of , which is centered at the origin.198.In the diagram below, is tangent to the circle at L.a. Find . Explain how you found your answer.b. Write an equation to find . Then solve for .c. State the theorem you used to set up your equation in part b.d. Find . Explain how you found your answer.e. Classify triangle MLP by its angles.199.Find in the diagram below.200.Find in the diagram below.201.Find the surface area of a sphere with a 12-foot radius in terms of ?.202.Find the surface area and volume of a hemisphere with an 8-inch diameter.Geometry Semester 2 Final Practice ProblemsAnswer SectionMULTIPLE CHOICE1.ANS:DREF:Lesson 13: Introduction to Triangles2.ANS:AREF:Lesson 13: Introduction to Triangles3.ANS:CREF:Lesson 13: Introduction to Triangles4.ANS:DREF:Lesson 16: Finding Slopes and Equations of Lines5.ANS:AREF:Lesson 17: More Conditional Statements6.ANS:BREF:Lesson 17: More Conditional Statements7.ANS:CREF:Lesson 17: More Conditional Statements8.ANS:AREF:Lesson 16: Finding Slopes and Equations of Lines9.ANS:DREF:Lesson 16: Finding Slopes and Equations of Lines10.ANS:BREF:Lesson 17: More Conditional Statements11.ANS:CREF:Investigation 3: Exploring Angles of Polygons12.ANS:DREF:Investigation 3: Exploring Angles of Polygons13.ANS:DREF:Investigation 3: Exploring Angles of Polygons14.ANS:DREF:Lesson 22: Finding Areas of Quadrilaterals15.ANS:AREF:Lesson 25: Triangle Congruence: SSS16.ANS:DREF:Lesson 26: Central Angles and Arc Measure17.ANS:CREF:Lesson 26: Central Angles and Arc Measure18.ANS:CREF:Lesson 22: Finding Areas of Quadrilaterals19.ANS:BREF:Lesson 22: Finding Areas of Quadrilaterals20.ANS:DREF:Lesson 23: Introduction to Circles21.ANS:AREF:Lesson 23: Introduction to Circles22.ANS:AREF:Lesson 23: Introduction to Circles23.ANS:DREF:Lesson 26: Central Angles and Arc Measure24.ANS:AREF:Lesson 26: Central Angles and Arc Measure25.ANS:AREF:Investigation 3: Exploring Angles of Polygons26.ANS:CREF:Investigation 3: Exploring Angles of Polygons27.ANS:BREF:Investigation 3: Exploring Angles of Polygons28.ANS:AREF:Investigation 3: Exploring Angles of Polygons29.ANS:BREF:Lesson 34: Properties of Parallelograms30.ANS:CREF:Lesson 34: Properties of Parallelograms31.ANS:DREF:Lesson 35: Finding Arc Lengths and Areas of Sectors32.ANS:AREF:Lesson 35: Finding Arc Lengths and Areas of Sectors33.ANS:DREF:Lesson 36: Right Triangle Congruence Theorems34.ANS:BREF:Lesson 36: Right Triangle Congruence Theorems35.ANS:BREF:Lesson 36: Right Triangle Congruence Theorems36.ANS:DREF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines37.ANS:AREF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines38.ANS:AREF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines39.ANS:CREF:Lesson 34: Properties of Parallelograms40.ANS:BREF:Lesson 36: Right Triangle Congruence Theorems41.ANS:DREF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines42.ANS:CREF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines43.ANS:BREF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines44.ANS:CREF:Lesson 41: Ratios, Proportions, and Similarity45.ANS:DREF:Lesson 41: Ratios, Proportions, and Similarity46.ANS:AREF:Lesson 43: Chords, Secants, and Tangents47.ANS:AREF:Lesson 43: Chords, Secants, and Tangents48.ANS:BREF:Lesson 44: Applying Similarity49.ANS:BREF:Lesson 47: Circles and Inscribed Angles50.ANS:AREF:Lesson 49: Introduction to Solids51.ANS:CREF:Lesson 41: Ratios, Proportions, and Similarity52.ANS:DREF:Lesson 42: Finding Distance from a Point to a Line53.ANS:AREF:Lesson 43: Chords, Secants, and Tangents54.ANS:DREF:Lesson 44: Applying Similarity55.ANS:BREF:Lesson 44: Applying Similarity56.ANS:AREF:Lesson 46: Triangle Similarity: AA, SSS, SAS57.ANS:AREF:Lesson 46: Triangle Similarity: AA, SSS, SAS58.ANS:DREF:Lesson 47: Circles and Inscribed Angles59.ANS:DREF:Lesson 47: Circles and Inscribed Angles60.ANS:BREF:Lesson 49: Introduction to Solids61.ANS:DREF:Lesson 50: Geometric Mean62.ANS:BREF:Lesson 50: Geometric Mean63.ANS:AREF:Investigation 6: Geometric Probability64.ANS:CREF:Lesson 51: Properties of Isosceles and Equilateral Triangles65.ANS:DREF:Lesson 52: Properties of Rectangles, Rhombuses, and Squares66.ANS:BREF:Lesson 55: Triangle Midsegment Theorem67.ANS:AREF:Lesson 56: 30°-60°-90° Right Triangles68.ANS:BREF:Lesson 59: Finding Surface Areas and Volumes of Prisms69.ANS:AREF:Lesson 60: Proportionality Theorems70.ANS:CREF:Lesson 51: Properties of Isosceles and Equilateral Triangles71.ANS:AREF:Lesson 52: Properties of Rectangles, Rhombuses, and Squares72.ANS:AREF:Lesson 53: 45°-45°-90° Right Triangles73.ANS:BREF:Lesson 55: Triangle Midsegment Theorem74.ANS:AREF:Lesson 56: 30°-60°-90° Right Triangles75.ANS:AREF:Lesson 56: 30°-60°-90° Right Triangles76.ANS:BREF:Lesson 59: Finding Surface Areas and Volumes of Prisms77.ANS:AREF:Lesson 59: Finding Surface Areas and Volumes of Prisms78.ANS:DREF:Lesson 59: Finding Surface Areas and Volumes of Prisms79.ANS:BREF:Lesson 60: Proportionality Theorems80.ANS:AREF:Investigation 6: Geometric Probability81.ANS:AREF:Investigation 6: Geometric Probability82.ANS:AREF:Lesson 62: Finding Surface Areas and Volumes of Cylinders83.ANS:AREF:Lesson 62: Finding Surface Areas and Volumes of Cylinders84.ANS:EREF:Lesson 64: Angles Interior to Circles85.ANS:BREF:Lesson 69: Properties of Trapezoids and Kites86.ANS:DREF:Lesson 70: Finding Surface Areas and Volumes of Pyramids87.ANS:DREF:Lesson 62: Finding Surface Areas and Volumes of Cylinders88.ANS:AREF:Lesson 62: Finding Surface Areas and Volumes of Cylinders89.ANS:CREF:Lesson 64: Angles Interior to Circles90.ANS:BREF:Lesson 67: Introduction to Transformations91.ANS:BREF:Lesson 68: Introduction to Trigonometric Ratios92.ANS:DREF:Lesson 68: Introduction to Trigonometric Ratios93.ANS:AREF:Lesson 68: Introduction to Trigonometric Ratios94.ANS:BREF:Lesson 70: Finding Surface Areas and Volumes of Pyramids95.ANS:DREF:Lesson 70: Finding Surface Areas and Volumes of Pyramids96.ANS:CREF:Lesson 71: Translations97.ANS:AREF:Lesson 71: Translations98.ANS:CREF:Lesson 73: Applying Trigonometry: Angles of Elevation and Depression99.ANS:AREF:Lesson 73: Applying Trigonometry: Angles of Elevation and Depression100.ANS:AREF:Lesson 73: Applying Trigonometry: Angles of Elevation and Depression101.ANS:AREF:Lesson 73: Applying Trigonometry: Angles of Elevation and Depression102.ANS:DREF:Lesson 75: Writing the Equation of a Circle103.ANS:CREF:Lesson 75: Writing the Equation of a Circle104.ANS:DREF:Lesson 77: Finding Surface Areas and Volumes of Cones105.ANS:AREF:Lesson 77: Finding Surface Areas and Volumes of Cones106.ANS:BREF:Lesson 77: Finding Surface Areas and Volumes of Cones107.ANS:DREF:Lesson 77: Finding Surface Areas and Volumes of Cones108.ANS:AREF:Lesson 79: Angles Exterior to Circles109.ANS:BREF:Lesson 79: Angles Exterior to Circles110.ANS:AREF:Lesson 80: Finding Surface Areas and Volumes of Spheres111.ANS:AREF:Lesson 80: Finding Surface Areas and Volumes of Spheres112.ANS:DREF:Lesson 80: Finding Surface Areas and Volumes of Spheres113.ANS:DREF:Lesson 71: Translations114.ANS:AREF:Lesson 75: Writing the Equation of a Circle115.ANS:CREF:Lesson 77: Finding Surface Areas and Volumes of ConesNUMERIC RESPONSE116.ANS:5.5REF:Lesson 13: Introduction to Triangles117.ANS:25REF:Investigation 2: Proving the Pythagorean Theorem118.ANS:2REF:Lesson 16: Finding Slopes and Equations of Lines119.ANS:8REF:Lesson 16: Finding Slopes and Equations of Lines120.ANS:570.5REF:Lesson 22: Finding Areas of Quadrilaterals121.ANS:12REF:Lesson 22: Finding Areas of Quadrilaterals122.ANS:64REF:Lesson 22: Finding Areas of Quadrilaterals123.ANS:90REF:Lesson 22: Finding Areas of Quadrilaterals124.ANS:36REF:Lesson 22: Finding Areas of Quadrilaterals125.ANS:37.68REF:Lesson 23: Introduction to Circles126.ANS:12.6REF:Lesson 23: Introduction to Circles127.ANS:113.04REF:Lesson 23: Introduction to Circles128.ANS:95REF:Lesson 23: Introduction to Circles129.ANS:6REF:Lesson 41: Ratios, Proportions, and Similarity130.ANS:2REF:Lesson 42: Finding Distance from a Point to a Line131.ANS:5REF:Lesson 42: Finding Distance from a Point to a Line132.ANS:4REF:Lesson 42: Finding Distance from a Point to a Line133.ANS:19REF:Lesson 42: Finding Distance from a Point to a Line134.ANS:6REF:Lesson 42: Finding Distance from a Point to a Line135.ANS:14REF:Lesson 44: Applying Similarity136.ANS:8.5REF:Lesson 44: Applying Similarity137.ANS:20%REF:Investigation 6: Geometric Probability138.ANS:9REF:Lesson 51: Properties of Isosceles and Equilateral Triangles139.ANS:34REF:Lesson 52: Properties of Rectangles, Rhombuses, and Squares140.ANS:51REF:Lesson 53: 45°-45°-90° Right Triangles141.ANS:15REF:Lesson 59: Finding Surface Areas and Volumes of Prisms142.ANS:192REF:Lesson 59: Finding Surface Areas and Volumes of Prisms143.ANS:30REF:Lesson 66: Finding Perimeters and Areas of Regular Polygons144.ANS:6.4REF:Lesson 68: Introduction to Trigonometric Ratios145.ANS:5.31REF:Lesson 70: Finding Surface Areas and Volumes of Pyramids146.ANS:23REF:Lesson 79: Angles Exterior to Circles147.ANS:18REF:Lesson 73: Applying Trigonometry: Angles of Elevation and Depression148.ANS:345REF:Lesson 73: Applying Trigonometry: Angles of Elevation and Depression149.ANS:373.85REF:Lesson 77: Finding Surface Areas and Volumes of Cones150.ANS:284.955REF:Lesson 80: Finding Surface Areas and Volumes of Spheres151.ANS:1017.88REF:Lesson 80: Finding Surface Areas and Volumes of SpheresPROBLEM152.ANS:y = x – REF:Lesson 16: Finding Slopes and Equations of Lines153.ANS:Hypothesis: ; Conclusion: ; Converse: The converse is not necessarily true.REF:Lesson 17: More Conditional Statements154.ANS:REF:Lesson 17: More Conditional Statements155.ANS: Both the statement and it inverse are true.REF:Lesson 17: More Conditional Statements156.ANS: if and only if . For the biconditional to be true, both the statement and its converse must be true. In this case, the converse, if then , is not true, so the biconditional is not true.REF:Lesson 20: Interpreting Truth Tables157.ANS:120°REF:Investigation 3: Exploring Angles of Polygons158.ANS:540°REF:Investigation 3: Exploring Angles of Polygons159.ANS:In these two triangles, A corresponds to X, B corresponds to Y, and C corresponds to Z. Therefore, .REF:Lesson 25: Triangle Congruence: SSS160.ANS:REF:Lesson 25: Triangle Congruence: SSS161.ANS:Sample: Central angles are Minor arcs are Major arcs are Two semi-circles are REF:Lesson 26: Central Angles and Arc Measure162.ANS:150°REF:Lesson 26: Central Angles and Arc Measure163.ANS:REF:Lesson 33: Converse of the Pythagorean Theorem164.ANS:The triangle is not a right triangle by the Converse of the Pythagorean Theorem.REF:Lesson 33: Converse of the Pythagorean Theorem165.ANS:Scalene; ObtuseREF:Lesson 33: Converse of the Pythagorean Theorem166.ANS:98°, 82°, 98°REF:Lesson 34: Properties of Parallelograms167.ANS:REF:Lesson 35: Finding Arc Lengths and Areas of Sectors168.ANS:112? square feetREF:Lesson 35: Finding Arc Lengths and Areas of Sectors169.ANS:y = x + 16REF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines170.ANS:REF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines171.ANS:REF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines172.ANS:REF:Lesson 37: Writing Equations of Parallel and Perpendicular Lines173.ANS:REF:Lesson 41: Ratios, Proportions, and Similarity174.ANS:a = 12; b = 30REF:Lesson 41: Ratios, Proportions, and Similarity175.ANS:??4.47 inchesREF:Lesson 43: Chords, Secants, and Tangents176.ANS:x = 6, y = 8REF:Lesson 44: Applying Similarity177.ANS:REF:Lesson 47: Circles and Inscribed Angles178.ANS:; ; REF:Lesson 47: Circles and Inscribed Angles179.ANS:Rectangular PyramidREF:Lesson 49: Introduction to Solids180.ANS:, REF:Lesson 50: Geometric Mean181.ANS:AD?=?, AB?=?REF:Lesson 50: Geometric Mean182.ANS:red: ; blue: ; yellow: REF:Investigation 6: Geometric Probability183.ANS:REF:Lesson 51: Properties of Isosceles and Equilateral Triangles184.ANS:REF:Lesson 51: Properties of Isosceles and Equilateral Triangles185.ANS: centimetersREF:Lesson 53: 45°-45°-90° Right Triangles186.ANS:, REF:Lesson 55: Triangle Midsegment Theorem187.ANS:, REF:Lesson 56: 30°-60°-90° Right Triangles188.ANS:REF:Lesson 56: 30°-60°-90° Right Triangles189.ANS:a. Sample:b. 54°c. By Theorem 58-1, is perpendicular to line m, so is a right angle. Therefore, is a right triangle. Therefore, and are complementary. d. 54°e. inchesREF:Lesson 58: Tangents and Circles, Part 1190.ANS:REF:Lesson 58: Tangents and Circles, Part 1191.ANS:REF:Lesson 60: Proportionality Theorems192.ANS:REF:Lesson 64: Angles Interior to Circles193.ANS:, , REF:Lesson 69: Properties of Trapezoids and Kites194.ANS:a.6036 m2S =?S = 854.865 + 5181S = 6035.865b.42,743 m3V = V = 42,743.25REF:Lesson 62: Finding Surface Areas and Volumes of Cylinders195.ANS:REF:Lesson 75: Writing the Equation of a Circle196.ANS:REF:Lesson 75: Writing the Equation of a Circle197.ANS:REF:Lesson 75: Writing the Equation of a Circle198.ANS:a. 168°; By the Arc Addition Postulate, . Substitute and simplify to find that is 168°.b. ; 60.5°c. Theorem 79-1 states, “The measure of an angle whose vertex is outside of a circle is equal to half the difference of the intercepted arcs.”d. 96°; ; Since , then by substitution and .e. obtuse triangleREF:Lesson 79: Angles Exterior to Circles199.ANS:REF:Lesson 79: Angles Exterior to Circles200.ANS:REF:Lesson 79: Angles Exterior to Circles201.ANS: square feetREF:Lesson 80: Finding Surface Areas and Volumes of Spheres202.ANS: cubic inches; square inchesREF:Lesson 80: Finding Surface Areas and Volumes of Spheres ................
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