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Name ___________________________________ Unit 3 β Geometry Review for Unit 3 Test (Aims #22-30) Date ______________ Math 8H 1) Complete each statement based on the diagram to the right where line AB is parallel to line CD and transversal EF intersects both lines. a) A pair of vertical angles are ___________ and ___________. b) A pair of alternate interior angles are ___________ and ___________. c) A pair of corresponding angles are ___________ and ___________. d) A pair of alternate exterior angles are ___________ and ___________. e) A pair of supplementary angles are ___________ and ___________. 2) Solve for the variable specified in each diagram. a) b) 3) In triangle PQR below, m ο P = 66°. a) What is the measure of side lengths. c) ο Q? b) Classify the triangle by its angles and 4) Given Line π¨π© is parallel to Line πͺπ¬, prove that the interior angles of triangle π¨π©πͺ have a sum of πππΛ. 5) Determine the measure of each of the missing angles in the diagram below. m ο 1 = ________ m ο 7 = ________ m ο 2 = ________ m ο 8 = ________ m ο 3 = ________ m ο 9 = ________ m ο 4 = ________ m ο 10 = ________ m ο 5 = ________ m ο 11 = ________ m ο 6 = ________ m ο 12 = ________ 6) What is the sum of the measures of the interior angles of a decagon? 7) What is the measure of one interior angle of a regular octagon? 8) What is the measure of one exterior angle of a regular hexagon? 9) Segment AB was dilated to AβBβ by a scale factor of 4. If AB = 3.5, what is the length of AβBβ? 10) In the diagram to the right, οXYZ οRST . a) What is the length of RT? b) What is the ratio of sides of triangle XYZ to triangle RST in simplest form? c) If triangle RST is the dilated image of triangle XYZ, then what is the scale factor? 11) In the diagram below, οABC οDEF . What is the length of DE? 12) Use the diagram to answer the questions that follow. The length of each segment is as shown: segment ππ is 5 units, segment ππ is 7 units, segment ππ is 3 units, and segment πβ²πβ² is 12.6 units. a) Suppose ππ is parallel to πβ²πβ². Is triangle Ξπππ similar to triangle Ξππβ²πβ²? Explain. b) What is the length of segment ππβ²? c) What is the length of segment ππβ²? 13) Two triangles are similar. The sides of the first triangle are 7, 9, and 11. The smallest side of the second triangle is 21. Determine the perimeter of the second triangle. 14) At a certain time of the day, the shadow of a 5' boy is 8' long. The shadow of a tree at this same time is 28' long. How tall is the tree? 15) Use the diagram to the right, to answer each question. Let m ο CFB = 125°. a) What is the m ο CFE? _________ b) What is the m ο AFC _________ c) What is the m ο AFD? _________ d) Name the angle vertical to ο CFB. _________ e) Name an angle adjacent to ο BFD. _________ f) Name an angle supplementary to ο AFC. _________ 16) Determine the measure of each angle in the diagram below. m ο 1 = ________ m ο 2 = ________ m ο 3 = ________ m ο 4 = ________ m ο 5 = ________ 17) What is the value of x in the diagram to the right? Explain how you know. 18) Use the diagram below to answer the following questions. a) Which angle is alternate exterior to ο 2? _______ b) Which angle is corresponding to ο 8? _______ c) Which angle is alternate interior to ο 3? _______ d) If the m ο 1 = 109°, then what is the m ο 7? Explain how you know. 19) True or False: An obtuse triangle has one or more obtuse angles. ___________ 21) Determine the value of each variable. a = _________ b = _________ c = _________ 22) What is the value of y in the diagram below? Show your work! 23) In the diagram below, determine the measure of angle KLJ. Explain in detail how you know you are correct.