A b c d a e d f g e h b c i f 6 6 60 5 3 13 ft 11 ft

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a. b. c. d. A e. D f. G E H B C I F 6 - 6 170 79 7.4 6.0 5 3 13 ft 11 ft 9 cm 16 cm 21 m 12 m
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MFM2P Date: ______________ Unit 6: Similar Triangles 6.2 Properties and Solving of Similar Triangles Investigation Side Lengths Using the dot paper, draw triangles XYZ with perpendicular sides lengths of 6 and 8 units. Draw triangle PQR with perpendicular side lengths of 12 and 16 units. Label each triangle accordingly. Determine the lengths of the hypotenuse of each of the triangles. ∆XYZ ∆PQR Indicate the length of each side of each triangle in the table below. ∆XYZ ∆PQR What do you notice about the side lengths? XY = PQ = YZ = QR = XZ = PR = 6 - 7
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MFM2P Date: ______________ Unit 6: Similar Triangles Investigation Angles Given the following triangles answer the questions below. Label each triangle. Indicate the angle measures of each triangle in the table below each triangle. ∆XYZ ∆PQR What do you notice about the measures of the angles in each of the triangles? X= P= Y= Q= Z= R= Corresponding sides and angles are similar in proportion. Therefore, Sides Angles XY corresponds with ___________. A corresponds with ___________. YZ corresponds with ___________. A corresponds with ___________. XZ corresponds with ___________. A corresponds with ___________. Since, we know what sides correspond let’s setup ratios. XY = = PQ = = = = Triangles are SIMILAR if: Corresponding _______________ are equal Corresponding _______________ are proportional in length The symbol _________ represents “is ____________________ to” 6 - 8 62⁰ 62⁰
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MFM2P Date: ______________ Unit 6: Similar Triangles 1. ∆PQR is similar to ∆JKL. Determine the lengths of KL and PR . 6.5 cm 19.5 cm P Q Q J K 4.3 cm 21cm R 15.6 cm Statement: L Set up ratios and fill in missing information: Consider the complete ratio and set it equal to one of the other ratios and solve for the unknown. Repeat previous step to solve for the other unknown. 2. ∆ZVB is similar to ∆ LAP. Determine the values of x and y . Z 18 m x 28m 24m V y B 3. ∆DEF is similar to ∆ABC. Determine the values of the missing angles. 6 - 9 ° ° A P L 27 m D E F A B C 43˚ 49˚
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MFM2P Date: ______________ Unit 6: Similar Triangles 6.2 Properties and Solving of Similar Triangles PRACTICE 1. Prove that ABC is similar to DEF. Show all of your work! a) A F E D B C E A b) F B C D 2. HIJ is similar to LMN. Determine the lengths of HJ and MN. H L I J M N 3. BOY is similar to CAT. Determine the values of x and y. B C O A T Y 4. LST is similar to UBM. Determine the values of the missing angles. L B U 6 - 10 * * 12 m 15 m 9 m 13.5 m 22.5 m 18 m 27 in 24 in 5.5 in 8 in 20.2 km y 17.6 km 8.8 km x 6.1 km 76˚ 53˚ SOLUTIONS: 1a) Corresponding angles are equivalent, so ∆ABC~∆DEF 2b) Corresponding side lengths are proportional (1.5), so ∆ABC~∆DEF 3.
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