1-5 skills practice angle relationships answer key pdf - pdf

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1-5 skills practice angle relationships answer key pdf - pdf

!5 3 5 1 T 2V Name the sides of each angle. Three angles are !1, !2, and !3. If m!FCG ! 9x $ 3 and m!GCB ! 13x % 9, find m!GCB. A good way to remember related geometric ideas is to compare them and see how they are alike and how they are different. P ! 84 kilometers 15. 129&18'36( 13. A D 3. ? Glencoe/McGraw-Hill 23 Glencoe Geometry Lesson 1-4 Reading the Lesson NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Enrichment Angle Relationships Angles are measured in degrees (&). !EBC Using a protractor, m!EBC ! 90. Mark eight equally-spaced points on each ray, and number the points as shown below. triangle ABC with vertices A(3, 5), B(3, 1), and C(0, 1) 11. Some terms in the second column may be used more than once or not at all. The angles form a linear pair. !TZW 14. opposite rays c. 9&2'32( 15. P ! 8s ii. a pair of acute vertical angles c. If two angles form a linear pair, one is acute and the other is obtuse. regular octagon f. Since !!" PN bisects !MPR, !MPN ! !NPR, or m!MPN ! m!NPR. NAME ______________________________________________ DATE ____________ PERIOD _____ Enrichment 1-5 Curve Stitching The star design at the right was created by a method known as curve stitching. b. Match each description in the first column with one of the terms in the second column. !1 3. TRAFFIC SIGNS The diagram shows a sign used to warn drivers of a school zone or crossing. In the figure at the right, #AC BD , # !" #!" or AC BD . COORDINATE GEOMETRY Find the perimeter of each polygon. P ! 96 6. A ray that divides an angle into two congruent angles is called an angle bisector. Name an angle supplementary to !FKG. !SRQ and !QRP is a linear pair. If m!EBF ! 7y % 3 and m!FBC ! 3y $ 3, find y so !" !!" that !EB BC . a ray that divides an angle into two congruent angles 8. If m!PTQ ! 3y % 10 and m!QTR ! y, find y so that !PTR is a right angle. 87&2'3( Two angles are supplementary if the sum of their measures is 180#. 4 B 3 2 C 3. 3. Name the sides of !BDC. Read the introduction to Lesson 1-6 at the top of page 45 in your textbook. Find m!MSN. !UZW 12. X Y Z U Lesson 1-5 12. When two perpendicular lines intersect, four congruent angles are formed. 12. m!DZQ $ m!QZP (9x $ 5) $ (3x $ 1) 12x $ 6 12x x ! ! ! ! ! m!DZP 90 90 84 7 D Q (9x " 5)# (3x " 1)# Sum of parts ! whole Substitution Z Simplify. P ! 26 inches 10. P ! 48 x 2x rectangle ? x x$2 x Glencoe/McGraw-Hill 2x 32 Glencoe Geometry NAME ______________________________________________ DATE 1-6 ____________ PERIOD _____ Skills Practice Name each polygon by its number of sides and then classify it as convex or concave and regular or irregular. K H 2. !NQO and !OQP are complementary. E D F B A C 5. Exercises !" #MQ !". Perimeter: P ! 2! $ 2w Area: A ! !w, where ! is the length and w is the width However, many figures are combinations of two or more rectangles creating irregular shapes. CE 15. If m!PQT ! 60 and m!PQS ! 4x $ 14, find the value of x. the common vertex of all angles shown in the figure k. Example Name each polygon by its number of sides. obtuse angles e. quadrilateral QRST with vertices Q(%3, 2), R(1, 2), S(1, %4), and T(%3, %4) 12. an acute angle d. !EBC is a right angle. P ! 6s c. If m!BGC ! 16x % 4 and m!CGD ! 2x $ 13, find x so that !BGD is a right angle. e. If m!DCE ! 4x $ 15 and m!ECF ! 6x % 5, find m!DCE. congruent angles f. !F and !G are two angles whose measures have a sum of 180. If m!2 ! 6y $ 2 and m!1 ! 8y % 14, find m!ABE. If Jasmine doubles the width of the scarf, how many inches of fringe will she need? 45&16'24( 11. Then classify it as concave or convex and regular or irregular. 15&54' 4. Is !DBF a right angle? !1 Measure each angle and classify it as right, acute, or obtuse. 98&52'59( 14. !UZT V W X U T Z Y !!" and CD !!" are opposite rays, ALGEBRA In the figure, CB !!" bisects !DCF, and CG !!" bisects !FCB. B 1 A A right angle is an angle whose measure is 90. !4 6. g. 4. Name all angles that have R as a vertex. 3 4 6Q S 5 R P S R V N U 6. Create your own design. 5 4 3N P 2 S !1 and !3 are nonadjacent angles formed by two intersecting lines. Find the measures of an angle and its complement if one angle measures 18 degrees more than the other. 5. Match each polygon in the first column with the formula in the second column that can be used to find its perimeter. E F 1. ? Glencoe/McGraw-Hill 28 Be aco n 11. A 7. 10. !NMP 14. 34&29'45( 6. Name two acute vertical angles. !MQN and !MQR are vertical angles. 1&2'3( ? Glencoe/McGraw-Hill 24 Glencoe Geometry NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Study Guide and Intervention Angle Relationships Pairs of Angles Adjacent angles are angles in the same plane that have a common vertex and a common side, but no common interior points. Exercises Identify each pair of angles as adjacent, vertical, and/or as a linear pair. 20 yd 9. Tell whether each statement is always, sometimes, or never true. N M S 4. Find the measures of two complementary angles if the difference in their measures is 18. !OMN Write another name for each angle. ? A semicircle is half a circle. !3 and !2 For Exercises 5?7, refer to the figure at the right. If two angles are supplementary and x is the measure of one of the angles, then the measure of the other angle is . !4 12. Explain. If two angles are adjacent angles, they form a linear pair. a tool used to measure angles 6. the common endpoint of the rays that form an angle 7. !MPR P 5. 120&18' 8. 7 mm 5. A B C 18. E a. an obtuse angle 28# 28# C c. Identify two acute adjacent angles. Example 1 S R 1 2 P Example 2 Measure each angle and classify it as right, acute, or obtuse. Find x. Describe two different angle relationships between the streets. !1 Write another name for each angle. quadrilateral LMNO with vertices L(%1, 4), M(3, 4), N(2, 1), and O(%2, 1) ALGEBRA Find the length of each side of the polygon for the given perimeter. !DBC Using a protractor, m!DBC ! 115. 13. Example Find the area of the figure at the right. !NMP 5 7 O 8 1 P Q 2 3 4 M N R Name the sides of each angle. the angle with the greatest measure Helping You Remember 3. ? Glencoe/McGraw-Hill 20 Glencoe Geometry NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Skills Practice Angle Measure For Exercises 1?12, use the figure at the right. (Do not use an angle whose interior includes part of another angle.) ? How many separate angles are formed if n lines intersect at a common point? Glencoe/McGraw-Hill 31 Glencoe Geometry Lesson 1-6 Polygons NAME ______________________________________________ DATE ____________ PERIOD _____ Study Guide and Intervention 1-6 (continued) Polygons Perimeter The perimeter of a polygon is the sum of the lengths of all the sides of the polygon. If m!MPN ! 2x " 14 and m!NPR ! x " 34, find x and find m!MPR. angle bisector b. Look up the nonmathematical meaning of supplementary in your dictionary. Example Identify each pair of angles as adjacent angles, vertical angles, and/or as a linear pair. The polygon has 5 sides, so it is a pentagon. !5 7. Name an angle complementary to !EKH. ? Glencoe/McGraw-Hill 25 Glencoe Geometry Lesson 1-5 1. h. 11. a figure made up of two noncollinear rays with a 1. Find the measures of the angles. 2x $ 14 ! x $ 34 2x $ 14 % x ! x $ 34 % x x $ 14 ! 34 x $ 14 % 14 ! 34 % 14 x ! 20 m!NPR ! (2x $ 14) $ (x $ 34) ! 54 $ 54 ! 108 Exercises !!" bisects !PQT, and QP !!" and QR !!" are opposite rays. !2 4 W 4. C B E 2. If a supplement of an angle has a measure 78 less than the measure of the angle, what are the measures of the angles? Find the supplement of each of the following angles. In the figure, !!" PN is the angle bisector of !MPR. To find the area of an irregular shape, it helps to separate the shape into rectangles, calculate the formula for each rectangle, then find the sum of the areas. Helping You Remember 4. A pair of adjacent angles whose noncommon sides are opposite rays is called a linear pair. P Subtract 6 from each side. !QPR 10. !8 4. There are special formulas for the perimeter of a square or a rectangle. angle d. If m!ABF ! 7x % 8 and m!EBF ! 5x $ 10, find m!EBF. Reading the Lesson 1. Assume you have sticks with a good variety of lengths. 3 cm 2.5 cm 5.5 ft square 3.5 cm 3. STREET MAPS Darren sketched a map of the cross streets nearest to his home for his friend Miguel. 39&21'54( 12. w ! P ! 4s ! 4(5) ! 20 cm P ! 2! $ 2w ! 2(3) $ 2(2) ! 10 ft Exercises Find the perimeter of each figure. If m!PQS ! 3x $ 13 and m!SQT ! 6x % 2, find m!PQT. Name an angle adjacent and supplementary to !DCB. !VZU is adjacent to !YZX. The common endpoint is the vertex. ? How many degrees are there in a quarter circle? !WTS NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Practice Angle Measure For Exercises 1?10, use the figure at the right. The sides that have a common endpoint must be noncollinear and each side intersects exactly two other sides at their endpoints. a point on !CBE h. Olive Ma in Glencoe Geometry NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Reading to Learn Mathematics Angle Relationships Pre-Activity What kinds of angles are formed when streets intersect? Find x and y so that #NR N 2. Find the perimeter of each figure. A polygon is named according to its number of sides. 16. !3 3. 35&15' 2. 12 m 4 in. two pairs of congruent angles 65# 2 3 4 1 b. Name four different shapes that can each be formed by four sticks connected to form a closed figure. P ! 88 feet 4w $ 1 w ? Glencoe/McGraw-Hill 33 Glencoe Geometry Lesson 1-6 Polygons NAME ______________________________________________ DATE 1-6 ____________ PERIOD _____ Practice Polygons Name each polygon by its number of sides and then classify it as convex or concave and regular or irregular. Give some similarities and differences between congruent segments and congruent angles. !2 Measure each angle and classify it as right, acute, or obtuse. a point in the exterior of !EBA f. !4 S 2. Describe the steps you used to find the perimeter in Exercise 1. P ! 2! $ 2w vi. Two angles are complementary. !QMO P Q O L M N !!" and BC !!" are opposite rays, ALGEBRA In the figure, BA !!" bisects !EBC, and BF !!" bisects !ABE. Name a linear pair. a pair of obtuse vertical angles d. ? Glencoe/McGraw-Hill 36 Glencoe Geometry 18 mm 6. !3 10. ALGEBRA For Exercises 9?10, use the figure at the right. 50 " 90, so !ABD is an acute angle. a right angle F D b. pentagon STUVW with vertices S(0, 0), T(3, %2), U(2, %5), V(%2, %5), and W(%3, %2) ALGEBRA Find the length of each side of the polygon for the given perimeter. b c 3 in. They are supplementary. Name two acute adjacent angles. Vertical angles are two nonadjacent angles formed by two intersecting lines. The two angles in a linear pair are both acute. P ! 104 millimeters 14. !YZU and !UZV are supplementary. They are adjacent angles. The right angle symbol indicates that the lines !" is perpendicular to #!" are perpendicular. A B 120# F 60# G !A and !B are two angles whose measures have a sum of 90. If m!FGE ! 5x $ 10, find x so that #FC !" #!" AE . Although the design appears to contain curves, it is made up entirely of line segments. 6. the sides of !ABF i. If two angles form a linear pair, they are complementary. Vertical angles are supplementary. D A R C 30# !6 and !5 are adjacent angles whose noncommon sides are opposite rays. 16 in. square i. Then classify it as concave or convex and regular or irregular. Name each of the following in the figure at the right. Measure each angle in the figure and classify it as right, acute, or obtuse. Point N lies in the interior of !MPR and !MPN ! !NPR. Find y, m!RPT, and m!TPW. m!EBF ! 3x $ 10, m!DBE ! x, and !BD 4. vertex common endpoint 2. Each degree of an angle is divided into 60 minutes ('), and each minute of an angle is divided into 60 seconds ((). Complete the section of the star design above by connecting pairs of points that have the same number. If m!RTS ! 8x $ 18, find x so that !!" TR TS 10. S T P 2. B C G F 8. The measure of the supplement of an angle is 36 less than the measure of the angle. Because it is concave, it cannot have all its angles congruent and so it is irregular. A ! !w A1 ! 9 * 2 ! 18 9m 2m 5m 3m A2 ! 3 * 3 !9 9m 1 2m 18 $ 9 ! 27 The area of the irregular shape is 27 m2. One way to remember the meaning of a term is to explain it to another person. Measure and classify each numbered angle. How many degrees are there in a semicircle? 84&12' 9. Q P T Determine whether each statement can be assumed from the figure. 5 cm s 3 ft ! s 5 cm 2 ft w s 5 cm P!a$b$c !3$4$5 ! 12 in. How would you explain to a friend what a regular polygon is? An acute angle has measure less than 90. Separate the figure into two rectangles. Exercises A 1. 8. 6 Name the vertex of each angle. !5 2. four linear pairs g. It is convex and is a regular octagon. P ! 12s e. 21 mi 10 mm 18 mm 33 mi 2 cm 14 cm 6 cm 4 cm 6 cm 6 cm 4 cm 14 cm 32 mi COORDINATE GEOMETRY Find the perimeter of each polygon. Jasmine plans to sew fringe around the scarf shown in the diagram. NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Study Guide and Intervention (continued) Angle Measure Congruent Angles Angles that have the same measure are congruent angles. !RPN R 6. Example Write an expression or formula for the perimeter of each polygon. If two angles are complementary, they are adjacent. G J 3. Read the introduction to Lesson 1-5 at the top of page 37 in your textbook. (s represents the length of each side of a regular polygon.) a. a 5 cm s 5 in. 9. !!" and BC !!" are opposite rays, BF !!" bisects !CBE, and BA !!" bisects !ABE. !2 and !4 are also vertical angles. 10 in. !1 and !6 V 2 1 3. For other angles, use three letters to name them: !SRQ, !PRT, and !SRT. 1 A 2 3 B F 4 C 4. 4 in. Read the introduction to Lesson 1-4 at the top of page 29 in your textbook. It is concave because part of D "E " or E "F " lies in the interior of the figure. ? 1. Complete each sentence. G H F 1. ALGEBRA For Exercises 7?8, use the figure at the right. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 To make a complete star, make the same design in six 60? angles that have a common central vertex. a pair of opposite rays j. ? Glencoe/McGraw-Hill 27 Glencoe Geometry NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Practice Angle Relationships For Exercises 1?4, use the figure at the right and a protractor. 60# 6 B 1 d. !ABD Using a protractor, m!ABD ! 50. Name the sides of !1. P ! 39 centimeters 11. a. the angle bisector of !EBC g. i. T 3 C Q E D a. 1 D 2. Complete the following design. Name each polygon by its number of sides. P 5x # M x# (9y " 18)# S Q R !" !BF !". QS 1. Find x, m!PQS, and m!SQR. 5m 2 3m Find the area and perimeter of each irregular shape. 11 12 13 14 15 16 17 18 19 1 11 2 12 3 13 4 14 5 15 6 16 7 17 8 18 9 19 1 2 3 4 5 6 7 8 9 3. Vertical angles are complementary. 1 in. right angles g. Name the vertex of !4. P Q M 10. Name two obtuse vertical angles. An obtuse angle has measure greater than 90 but less than 180. 2. !NPS ? Glencoe/McGrawHill 19 Glencoe Geometry Lesson 1-4 Refer to the figure. If m!EBD ! 4x $ 16 and m!DBC ! 6x $ 4, find m!EBD. !6 6. !1 and !2 T U NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Study Guide and Intervention (continued) Angle Relationships Perpendicular Lines Lines, rays, and segments that form four right angles are perpendicular. quadrilateral OPQR with vertices O(%3, 2), P(1, 5), Q(6, 4), and R(5, %2) 8. If two angles are complementary and x is the measure of one of the angles, then the measure of the other angle is . BD E F D 17. a pair of congruent angles l. angles whose degree measures are between 90 and 180 5. 2 in. All sides are congruent and all angles are congruent, so it is a regular pentagon. The measure of one angle is 21 more than twice the measure of the other angle. The angle at the right can be named as !A, !BAC, !CAB, or !1. Write another name for !DBC. What is another name for a regular quadrilateral? F H L I G J The polygon has 4 sides, so it is a quadrilateral. S T U M R !SRT and !TRU have a common vertex and a common side, but no common interior points. It is convex. 27&16' 3. 180 # 115 # 90, so !DBC is an obtuse angle. f. Divide each side by 12. !WZU is a right angle. (Do not count an angle whose interior includes part of another angle.) Reading the Lesson 1. 26 m 6 cm 2 cm 4. 4 cm 7 ft 3 ft 4 cm 6 ft 2 ft 2 cm 4 cm 9m 7m 9 ft 4 cm 4 ft 8 cm For Exercises 5?8, find the perimeter of the figures in Exercises 1?4. !MOP 8. rectangle iv. !!", RP !!" RS b. four pairs of supplementary angles 2. 13 m 6m 2 in. 7. two pairs of vertical angles f. Then connect pairs of points that have the same number. !OMN 15. regular dodecagon b. compass 10. R S 12. N O 9. Find the complement of each of the following angles. S W V 11. a point in the interior of !EBC A B G e. triangle v. D E Determine whether each statement can be assumed from the figure. 6m 4m 20 yd 18 yd 40 yd 2m 3m 5m 2 in. K The figure is not closed, so it is not a polygon. A regular polygon has congruent sides and congruent angles. Then classify it as convex or concave and regular or not regular. You may use several angles, and the angles may overlap. D E C F G B 2 1 ? Glencoe/McGraw-Hill 22 Glencoe Geometry NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Reading to Learn Mathematics Angle Measure Pre-Activity How big is a degree? ? Glencoe/McGraw-Hill 30 Glencoe Geometry NAME ______________________________________________ DATE ____________ PERIOD _____ Study Guide and Intervention 1-6 Polygons A polygon is a closed figure formed by a finite number of coplanar line segments. 29&18'22( 5. ? Glencoe/McGraw-Hill 34 Glencoe Geometry NAME ______________________________________________ DATE 1-6 ____________ PERIOD _____ Reading to Learn Mathematics Pre-Activity How are polygons related to toys? !STV 8. T (4y $ 5)# (2y " 5)# R P W V S ? Glencoe/McGraw-Hill 26 Glencoe Geometry NAME ______________________________________________ DATE 1-5 ____________ PERIOD _____ Skills Practice Angle Relationships For Exercises 1?6, use the figure at the right and a protractor. Tell why each figure is not a polygon. angles that have the same measure 4. They are complementary. !1 and !5 4. How can this definition help you to remember the meaning of supplementary angles? P ! 89 feet 3x " 5 6n $ 8 2x " 2 2x $ 3 n x"9 5x $ 4 SEWING For Exercises 12?13, use the following information. M N P R Q R Example Refer to the figure above. To begin the star design, draw a 60? angle. A polygon can be concave or convex. BD E D 3. 110&2' 10. If " DZ "P "Z ", then m!DZP ! 90. protractor 2. regular hexagon iii. c. R !!". T 8. ? Glencoe/McGraw-Hill 29 Glencoe Geometry Lesson 1-5 b. d. A B C D Example Find x so that D !Z !P !Z !. Identify an angle supplementary to !TNU. 60' ! 1& 60( ! 1' 1 2 67))& ! 67&30' 70.4& ! 70?24' 90& ! 89?60' Two angles are complementary if the sum of their measures is 90#. P ! a $ b $ c d. The figure has 8 congruent sides and 8 congruent angles. U Name the vertex of each angle. P ! 4s Helping You Remember 5. Exercises Name each polygon by its number of sides. Name an angle not adjacent to but complementary to !FGC. Transcript NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Study Guide and Intervention Angle Measure Measure Angles If two noncollinear rays have a common endpoint, they form an angle. four pairs of adjacent angles e. How many inches of fringe does she need to purchase? 17. D E b. The rays are the sides of the angle. Find the perimeter. 27 yd 19 yd 1 cm 14 yd 12 yd 24 yd Find the length of each side of the polygon for the given perimeter. If m!1 ! 4x $ 10 and m!2 ! 5x, find m!2. A B C a. ? Glencoe/McGraw-Hill 21 Glencoe Geometry Lesson 1-4 11. If m!EBF ! 6x $ 4 and m!CBF ! 7x % 2, find m!EBC. angles whose degree measures are less than 90 3. !2 7. Identify two obtuse vertical angles. They are vertical angles. Name a linear pair whose vertex is B. P S 3x # (8x " 2)# Q R 6. ? How many separate angles are formed if three lines intersect at a common point? acute angles 9. !QMN 16. Use the figure to name each of the following. If two angles are supplementary, they are congruent. !YZW 13. ? Glencoe/McGraw-Hill 35 Glencoe Geometry Lesson 1-6 Polygons NAME ______________________________________________ DATE ____________ PERIOD _____ Enrichment 1-6 Perimeter and Area of Irregular Shapes Two formulas that are used frequently in mathematics are perimeter and area of a rectangle. 1.

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