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Triangle Congruence and ProofsObjective: You will be asked to…SectionProblem #Note to Self1. Classify polygons1.61-42Find the measure of interior and exterior angles of polygons.6.15-123.Name congruent polygons.4.313-164.Find missing side lengths and angle measures of congruent polygons.4.313-165.Use SSS and SAS to show that triangles are congruent.4.417-236.Use ASA and AAS to show that traingles are congruent4.517-237.Use algebra to write two column proofs.2.6248.Use triangle congruency theorems to write two column geometric proofs.2.824TransformationsObjective: You will be asked to…SectionProblem #Note to Selfidentify transformations as reflections, rotations, translations4.725reflect points over a line9.126-32describe a reflection and find the line of reflection9.126-32translate points if given vector notation or function notation9.226-32describe a translation using vector notation or function notation9.226-32rotate points (90, 180, or 270 degrees) around the origin9.326-32describe a rotation9.326-32SimilarityObjective: You will be asked to…SectionProblem #Note to Selfwrite and solve proportions7.134-37use proportions to identify similar polygons7.234-37solve problems using the properties of similar polygons7.234-37identify similar triangles7.340-43solve problems using similar triangles7.340-43Right TrianglesObjective: You will be asked to…SectionProblem #Note to Selfuse 45-45-90 right triangles to solve problems8.345-48use 30-60-90 right triangles to solve problems8.345-48dilate a figure using a given scale factor and center of dilation9.633predict and apply the relationship between the scale factor and side lengths9.644AreaObjective: You will be asked to…SectionProblem #Note to Selfidentify and use parts of circles10.160-61find the measure of central angles and arcs10.155calculate the area of parallelograms and triangles11.149-50, 52calculate the area of trapezoids, kites, and rhombi11.251calculate the circumference and area of circles11.353-54calculate the area of sectors11.355calculate the area of regular polygons11.456calculate the area of composite figures11.457, 62use ratios to calculate the perimeter and area of similar figures11.558-593-D FiguresObjective: You will be asked to…SectionProblem #Note to Selfcalculate the lateral area and surface area of a prism12.263, 65calculate the lateral area and surface area of a cylinder12.267, 73calculate the lateral area and surface area of a pyramid12.364, 68, 70calculate the lateral area and surface area of a cone12.369calculate the volume of a prism12.463, 66calculate the volume of a cylinder12.467, 73calculate the volume of a pyramid12.564, 68, 70calculate the volume of a cone12.569calculate the surface area of a sphere12.671, 72calculate the volume of a sphere12.671, 72To Help You ReviewPractice problems are in this packet.Review past tests and quizzes to find areas where you need improvementRaise specific questions or ask to see specific problems during the reviewAs part of the review, we will go over problems that students request (as time permits).Review the attached study and test-taking tipsStudy TipsGet help ASAP. Do not wait until the day before an assessment to see the teacher for extra help. If you show up with questions regarding 12 different topics, and there are several other students seeking help, you might not be able to get all your questions cleared up.Do not wait until the night before to start studying. If you wait, you might not be able to ask your teacher for help if you have trouble. The more prepared you are, the less stress you should feel during the plete any practice tests. These are found in most textbooks. If no practice test is available, try a few problems from each relevant section/topic. Try them under test conditions (no notes, quiet environment, set amount of time). Check your answers with the back of the book. Bring SPECIFIC questions to your teacher.Try the teacher’s examples on your own. Check and compare your work to the teacher’s solutions from the notes. Bring SPECIFIC questions to your teacher.Review notes for all sections and topics. Be sure you understand the definitions, rules, formulae, processes, strategies, and examples. Bring SPECIFIC questions to your teacher.Make and study flashcards. Include:Subject of CardFrontBackVocabularyWordDefinition & pictureTheorems / PostulatesNameWording & picturePropertiesNameWording & exampleFormulaeFormulaWhat each variable representsNecessary units of measureProcessWhat the type of problem is called or what it looks likeSteps on how to solve it (put in your own words, if desired)StrategiesTopic of problemStrategies talked about in classCommon errorsTopic of problemThings to watch out forAvoid some stress: On the day of the assessment, do not talk to other students about it unless you think they can clarify a problem you are having.Test-Taking TipsBring a calculator with which you are familiar. While dividing decimals by hand is noble, it eats up your time and takes your focus away from the test material.Use a pencil and eraser. Crossing out mistakes leaves you with work that may be difficult for you to read.Write as neatly as possible. Many students misread their own writing. Also be sure you have correctly copied all the information from the problem.Write information down as soon as you get the test. Write formulae, rules, etc. somewhere on the test so you do not forget them later.Read the instructions carefully. Be sure you are answering the question being asked, and that you are answering all parts. You are not always just solving for X.Do the easy problems first. This lets you spend more time on difficult problems. If you are prepared, some of the problems (vocabulary, fill-ins, etc.) should be very quick to complete. Do problems in this order: easy problems, problems with the highest point value, then do the remaining problems.Do not spend too much time on one problem. Go back if you get stuck. Something that comes up later in the test may help you.Remember the questions the teacher asks the class when solving similar problems. It’s easy to “get it” in class because the teacher leads you to the solution with these questions. Lead yourself with these same questions.Check your work and your answers when you finished the test. Plug answers back into equations. Check to make sure your answers are reasonable and/or realistic: Could the length of a ladder really be -0.5ft?Final Exam InformationCheck weekly syllabus for date/time of final examBring a #2 pencil, calculator, and something to read (in case you finish early).You will be given a copy of the formula sheet that is attached at the end of this guideFinal Exam Breakdown: Non-Calculator:~ 14 multiple choiceCalculator:~ 27 short answer~1 open responseYour Final Exam grade is 10% of your grade for the entire year.1. Is the figure a polygon? If not, tell why.a.b.c.d.Find a polygon in each photograph. Classify the polygon.2.3.4.Solve for each variable.5.6.7.The sum of the measures of the angles of a regular polygon is 4500. How many sides does the polygon have?Exactly four angles of a hexagon are congruent. The other two angles are complementary. What is the measure of one of the four congruent angles?What is the sum of the measures of the interior angles of a 25-gon?What is the measure of an exterior angle of a regular polygon with 36 sides?How many sides are in a regular polygon whose exterior angles measure 15°?Find the value of the variables.Find the perimeter of PMYKF.?HLN ?GST, mH = 66°, and mS = 42°. What is mT?Is ?ABC ?XYZ? Explain.Can you prove each pair of triangles is congruent? Show work by marking your diagram.If you can prove it:Tell what theorem you would use (name one theorem only)Name the congruent trianglesName all pairs of congruent parts that support your theoremIf you can NOT:Write “Not possible” on line “a”.24. Given: JL bisects ∠KLMProve: ?JKL??JMLStatementReason 1.∠K?∠M1.2.JK?JM2.3.JL bisects ∠KLM3.4.∠KLJ?∠MLJ4.5.?JKL??JML5.Transformations25. Identify the type of congruence transformation shown as a reflection, translation, or rotation.Graph each pair of triangles with the given vertices. Then, identify the transformation. A(2, 2), B(4, –1), C(1, –2); M(–4, –1), N(–1, –2), P(–2, 2) A(–1, –1), B(–1, –4), C(2, –4); M(–1, 1), N(–4, 1), P(–4, 4)Graph each figure and its image under the given reflection.ΔABC with vertices A(–1, –4), B(–5, 3), and C(0, 5) in the line y = xquadrilateral WXYZ with vertices W(–3, –2), X(–4, 1), Y(1, 4), and Z(2, –2) in the y-axisGraph each figure and its image after the specified rotation about the origin.ΔPQR with vertices P(–1, –2), Q(–5, –4), and R(–3, –6)? 90°parallelogram WXYZ with vertices W(–3, 3), X(–2, 7), Y(4, 5) and Z(3, 1)? 180°Graph each figure with the given vertices and its image after the indicated translation.Find the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor.ΔDEF: D(–5, 1), E(–3, 5), F(0, 3) Translation: along <4, 3>A(–5, –4), B(–2, –3), C(–1, –6), D(–4, –8); k = 12 Similarity & Right TrianglesDetermine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning.Each pair of polygons is similar. Find the value of x.Determine whether the triangles are similar. If so, write a similarity statement.When Rachel stands next to her cousin, Rachel’s shadow is 2 feet long and her cousin’s shadow is 1 foot long. If Rachel is 5 feet 6 inches tall, how tall is her cousin?Jason wants to determine if his foosball table is a dilation of his school’s soccer field. The dimensions of the table are 30 inches by 55.5 inches, and the dimensions of the field are 60 yards by 110 yards. Is the table a dilation? Explain.Find x.AreaFind the perimeter and area of each figure. Round to the nearest tenth if necessary.The height of a parallelogram is three times its base. If the area of the parallelogram is 108 square meters, find its base and height.Find the indicated measure. Round to the nearest tenth.The area of a circle is 201 square meters. Find the radius.Find the diameter of a circle with an area of 79 square feet.Find the area of the sector.Find the area of a regular hexagon that has an apothem of 63 cm and a side length of 12 cm.Find the area of the composite figure below.The pentagons are similar. Find the area of the small pentagon.The triangles are similar find x.CirclesIn circle M, MZ = 12 and WY = 20. Find each measure. Round to the nearest hundredth.CMXCQuadrilateral ABCD is circumscribed about H. Find m.3D FiguresFind the lateral area, surface area, and volume of the figure on the right.Find the lateral area, surface area, and volume of the figure on the right.Sarah has a fish tank with the dimensions shown.What is the surface area of the fish tank?If Sarah fills the tank to a depth of 17 inches, what will be the volume of the water in the tank?Find the lateral area, surface area, and volume of the figure on the right.Find the lateral area, surface area, and volume of the square pyramid on the right.Find the lateral area, surface area, and volume of the figure on the right.Find the lateral area, surface area, and volume of the figure on the right.Find the surface area and volume of the figure on the right.Find the surface area and volume of the figure on the right.An office has recycling barrels that are cylindrical with cardboard sides and plastic lids and bases. Each barrel is 3 feet tall with a diameter of 30 inches. How many square feet of cardboard are used to make each barrel? ................
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