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LESSON 6.2 Assignment Name me Date te Similar Triangles or Not? Similar Triangle Theorems ‹___› ‹___› 1. In the figure below, NS || BE . Use the information given in the figure to determine the m/SNA, m/NAS, m/ABE, and m/BAE. Is nNSA similar to nEBA? If the triangles are similar, write a similarity statement. Use complete sentences to explain your answers. B N A 328 858 E S The measure of angle SNA is 328, because alternate interior angles between parallel lines have the same measure. © Carnegie Learning The measure of angle ABE is 858, because alternate interior angles between parallel lines have the same measure. The measure of angle NAS and the measure of angle BAE is 638, because vertical angles are congruent. The sum of the measures of the interior angles in a triangle is 1808. So, m/NAS 5 m/BAE 5 1808 2 858 2 328 5 638. Therefore, nNSA , nEBA because of Angle-Angle Similarity Postulate. 6 Chapter 6 Assignments 119 LESSON 6.2 Assignment page 2 2. Use a ruler to determine whether the triangles shown are similar. Explain your answer. E DE = 1.5 cm D EF = 6 cm F DF = 7 cm AC = 14 cm C A AB = 3 cm BC = 12 cm B ___ ___ ___ All of the corresponding sides are proportional: 3 5 12 5 14 5 2. 1.5 7 6 © Carnegie Learning So, the triangles are similar by the Side-Side-Side Similarity Postulate. 6 120 Chapter 6 Assignments LESSON 6.2 Assignment page 3 Name me Date te ___ ___ 3. In the figure shown, NU || CV . Use the figure to complete part (a) through part (c). M U N V C a. Is /MUN > /MCV ? Explain your answer. Yes. Segments NU and CV are parallel and angles MUN and MCV are corresponding angles. When two parallel lines are intersected by a transversal, then the corresponding angles are congruent. So, angles MUN and MCV are congruent. b. Is /MNU > /MVC ? Explain your answer. © Carnegie Learning Yes. Segments NU and CV are parallel and angles MNU and MVC are corresponding angles. When two parallel lines are intersected by a transversal, then the corresponding angles are congruent. So, angles MNU and MVC are congruent. 6 c. Is nCMV , nUMN ? Explain your answer. Yes. Angles MUN and MCV are congruent and angles MNU and MVC are congruent, so by the Angle-Angle Similarity Postulate nCMV , nUMN. Chapter 6 Assignments 121 LESSON 6.2 Assignment page 4 4. In the figure shown, segments AB and DE are parallel. The length of segment BC is 10 units and the length of segment CD is 5 units. Use this information to calculate the value of x. Explain how you determined your answer. 2x + 5 D E 5 C 10 A B 11x – 4 Segments AB and DE are parallel, so by the Corresponding Angles Postulate angles A and E are congruent and angles B and D are congruent. In addition, by the Vertical Angles Congruence Postulate angles DCE and BCA are congruent because they are vertical angles. So, by the AngleAngle Similarity Postulate triangles ACB and ECD are similar and the ratios of the corresponding side lengths are equal. 10 11x 2 4 5 ___ ________ 5 2x 1 5 5(11x 2 4) 5 10(2 x 1 5) 55x 2 20 5 20x 1 50 35x 5 70 x52 © Carnegie Learning So, the value of x is 2 units. 6 122 Chapter 6 Assignments