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Unit 3: Geometry Name: ______________________ Quiz (Lessons 1 to 4) Date: ________________ 1. Identify the object as a line, ray, or line segment. Name the object. a) b) D B c) E C A F ______________________ ______________________ 2. a) Name and measure the angles marked with arcs. ______________________ M N i) __________ = _______ ii) __________ = _______ Bonus► Name the quadrilateral in three ways. ______________________________ G H 3. Mark the parallel sides and the right angles. Then identify the type of quadrilateral. a) b) ______________________ c) ______________________ ______________________ 4. a) Use a protractor and the given line segment to draw ABC = 42. COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC b) Draw a line perpendicular to AB through point A. B A Sample Unit Quizzes and Tests for AP Book 8.1 K-35 Unit 3: Geometry Answer Key Quiz (Lessons 1 to 4) 1. a) line segment AD or line segment DA 2. b) line BE or line EB c) ray FC a) i) GMN = 112º ii) NHM = 62º Bonus Answers will vary. Sample answer: MNHG, MGHN, NMGH 3. a) rectangle b) trapezoid c) parallelogram Teacher to check. COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC 4. K-36 Sample Unit Quizzes and Tests for AP Book 8.1 Unit 3: Geometry Name: ______________________ Quiz (Lessons 5 to 8) Date: ________________ 1. Find the measure of the missing angle. A a) H b) B 58º D 23º 35º O C ______________________________ _____________________________ ______________________________ _____________________________ ______________________________ _____________________________ 2. One angle of an isosceles triangle is 36. Find the measures of the other angles. Hint: Make sketches to show the different options for placing the 36 angle. 3. Write “true” or “false.” If the statement is false, give a counterexample. COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC a) The opposite angles in any parallelogram are equal. b) All scalene triangles are right triangles. Bonus► Triangle MNO has M = 90, and N = 45. Classify the triangle. Sample Unit Quizzes and Tests for AP Book 8.1 K-37 Unit 3: Geometry Answer Key Quiz (Lessons 5 to 8) 1. a) B = 180º − (90º + 58º) = 180º − 148º = 32º b) H = 180º − (23º + 35º) = 180º − 58º = 122º 2. A triangle with angles 36º, 36º, and 108º. A triangle with angles 36º, 72º, and 72º 3. a) true b) false Counterexamples may vary. Teacher to check. Bonus O = 180º − 90º − 45º = 45º COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC MNO is a right isosceles triangle. K-38 Sample Unit Quizzes and Tests for AP Book 8.1 Unit 3: Geometry Name: ______________________ Test (Lessons 1 to 8) Date: ________________ 1. Match the diagram to the correct description. A. B. C. a) The rays intersect. ______ b) If the rays are extended far enough, they intersect. ______ c) The rays do not intersect, even if they are extended. ______ 2. a) Draw lines perpendicular to CD through points M and N. Label the intersection points. M N D C b) Draw line segment MN. Name the quadrilateral you created. ______________________ c) Classify the quadrilateral. __________________________________ 3. Measure the sides and the angles in the polygon. Mark the equal sides and equal angles. Then classify the polygon. Be as specific as you can. COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC a) b) ___________________________ Sample Unit Quizzes and Tests for AP Book 8.1 _____________________________ K-39 Unit 3: Geometry continued Test (Lessons 1 to 8) 4. Find the measure of the missing angle. a) A 23º B b) P 28 R C Q 5. One side of an isosceles triangle is 5 cm. The perimeter of the triangle is 13 cm. What are the lengths of the sides of the triangle? Make sketches to show the different options for placing the side that is 5 cm long. 6. If the statement is true, explain why. If the statement is false, give a counterexample. a) If a triangle is equilateral, its angles are all equal to 60. COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC b) A trapezoid cannot have two equal opposite sides. Bonus► Can a triangle have two right angles? Explain. K-40 Sample Unit Quizzes and Tests for AP Book 8.1 Unit 3: Geometry Answer Key Test (Lessons 1 to 8) 1. 2. a) A b) C b) c) B a) Teacher to check. b) Sample answer: CMND c) trapezoid or Sample counterexample: right trapezoid 3. a) false 29 mm 29 mm 137º 43º 43º 137º 29 mm 29 mm Bonus No. The angles in a triangle add to 180º. If two of the angles are right angles, then 90º + 90º = 180º, so the third angle measures zero. This doesn’t make a triangle. rhombus b) 26 mm 95º 4 cm 32º 53º 5 cm scalene obtuse triangle 4. a) A = 180º − (28º + 90º) = 180º − 118º = 67º b) R + Q = 180º − 28º = 152º R = Q = 152º ÷ 2 = 76º 5. 5 cm 5 cm 3 cm 4 cm 4 cm 5 cm 6. a) true COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC Sample answer: The angles in an equilateral triangle are all equal. The sum of the angles in a triangle is 180º, so each angle equals 180º ÷ 3 = 60º. Sample Unit Quizzes and Tests for AP Book 8.1 K-41 Unit 3: Geometry Name: ______________________ Quiz (Lessons 9 to 12) Date: ________________ B 1. The triangles shown are congruent. Identify the equal sides and equal angles. Then write the congruence statement. __________ = __________, __________ = __________, __________ = __________, __________ = __________, A D F __________ = __________, __________ = __________ Congruence statement: __________________________ C E 2. a) What is the measure of DBC? _____ How do you know? A 4.9 cm 3 cm 70 B E 5 cm C 5 cm b) Write the pairs of equal sides and equal angles in triangles AEB and BCD. 3 cm 75 __________ = __________ D __________ = __________ __________ = __________ Triangles AEB and BCD are congruent by the _______ congruence rule. c) DC = _____ = _____ cm d) Which angle in AEB equals BDC? _______ What is the measure of these angles? _______ COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC Bonus► What is the measure of the third pair of angles in triangles AEB and BCD? Explain. K-42 Sample Unit Quizzes and Tests for AP Book 8.1 Unit 3: Geometry Answer Key Quiz (Lessons 9 to 12) 1. AB = FE BD = EC AD = FC A = F B = E D = C △ABD ≅ △FEC 2. a) 70º DBC and ABE are vertical angles, so they are equal. b) BE = CE AB = DB ABE = DBC SAS c) AE, 4.9 d) EAB 75º Bonus Angles in a triangle add to 180º, so E = 180º − (A + EAB) = 180º − (75º + 70º) = 35º COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC △AEB ≅ △DCB, so E = C, so C = 35º Sample Unit Quizzes and Tests for AP Book 8.1 K-43 Unit 3: Geometry Name: ______________________ Quiz (Lessons 13 to 16) Date: ________________ 1. Find the missing angle. Show your work a) b) 76 29 x x x = ______ x = ______ 2. Find the missing alternate, corresponding, supplementary, or vertical angles. a) b) 46 61 y x y x = ______, y = ______ x = _______, y = ______ 3. Lines ℓ and m are parallel. Use what you know about corresponding and supplementary angles to explain why x + y = 180°. ℓ x m y z A Bonus► Zara says that AE is parallel to CD. Is she correct? Explain. 1.5 in 2 in B E C 2 in 1.5 in D K-44 Sample Unit Quizzes and Tests for AP Book 8.1 COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC x Unit 3: Geometry Answer Key Quiz (Lessons 13 to 16) 1. a) x = 90º + 29º = 119º b) x = 76º ÷ 2 a) x = 61º = 38º 2. y = 119º b) x = 46º y = 134º 3. z and x are corresponding angles, so z = x. y and z are supplementary angles, so y + z = 180º. y + x = y + z = 180º Bonus Yes. ABE = DBC since they are vertical angles. AB = BD and EB = CB COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC By the SAS rule, △ABE ≅ △DBC, so EAB = CDB. These are alternate angles at lines AE and CD. When alternate angles are equal, lines are parallel, so AE ∥ CD. Sample Unit Quizzes and Tests for AP Book 8.1 K-45 Unit 3: Geometry Name: ______________________ Test (Lessons 9 to 16) Date: ________________ 1. Use the congruence statement ABC XYZ PQR and A = 50, Y = 60 to find the measures of all angles in all three triangles. 2. Identify the congruence rule that tells you that the pair of triangles is congruent. a) b) Congruence rule: _______ c) Congruence rule: _______ Congruence rule: _______ 3. Fill in all the missing angles. Mark parallel lines if they are not marked already. a) b) c) 69 55 69 113 53 58 135 4. Use congruent triangles to explain why MON is isosceles. O M K-46 L N Sample Unit Quizzes and Tests for AP Book 8.1 COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC 69 Unit 3: Geometry continued Test (Lessons 9 to 16) 5. Are the quadrilaterals congruent? Use a ruler and a protractor to check. If yes, write the pairs of corresponding equal sides and corresponding equal angles. Then write the congruence statement. W B C U A D V X Bonus► Use the grid to draw a counterexample to this statement: If triangles ABC and DEF have AB = DE, BC = EF, and A = D, they are congruent. COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC Hint: Sketch the triangles first. Sample Unit Quizzes and Tests for AP Book 8.1 K-47 Unit 3: Geometry Answer Key Test (Lessons 9 to 16) 1. A = X = P = 50º B = Y = Q = 60º C = Z = R = 180º − (50º + 60º) Bonus Answers may vary. Teacher to check. Sample answer: = 180º − 110º = 70º 2. 3. a) ASA b) SAS c) SSS a) 111 69 69 111 67 113 111 69 b) B A C E 69 111 125 55 125 55 125 55 D F 135 45 45 c) 111 69 58 69 53 58 122 4. ML = NL LO = OL MLO = NLO = 90º By the SAS rule, △MOL ≅ △NOL, so MO = NO and △MON is isosceles. AB = WU COPYRIGHT © 2015 JUMP MATH: TO BE COPIED. CC 5. BC = UX CD = XV AD = WV A = W B = U C = X D = V ABCD ≅ WUXV K-48 Sample Unit Quizzes and Tests for AP Book 8.1