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5.1 ESSENTIAL QUESTION How do you identify congruent triangles and its corresponding parts?

VOCABULARY When two triangles have exactly the same size and shape, the sides and angles that are the same in the triangles are called corresponding parts. When all pairs of corresponding angles are congruent and all pairs of corresponding sides are congruent in two figures, the figures are congruent.

Given that JKL  RST, list All corresponding congruent parts. Example 1 List Corresponding Parts Given that JKL  RST, list All corresponding congruent parts. SOLUTION Which angles and sides correspond to each other? Corresponding Angles ∆JKL  ∆RST, so J  R. Corresponding Sides ∆JKL  ∆RST, so JK  RS. ∆JKL  ∆RST, so K  S. ∆JKL  ∆RST, so KL  ST. ∆JKL  ∆RST, so L  T. ∆JKL  ∆RST, so JL  RT. 4

The two triangles are congruent. Example 2 Write a Congruence Statement The two triangles are congruent. a. Identify all corresponding congruent parts. b. Write a congruence statement. SOLUTION a. Corresponding Angles A  F Corresponding Sides AB  FD B  D BC  DE C  E AC  FE 5

In the diagram, PQR  XYZ. Example 3 Use Properties of Congruent Triangles In the diagram, PQR  XYZ. Find the length of XZ. Find mQ. a. b. SOLUTION a. Because XZ  PR, you know that XZ = PR = 10. b. Because Q  Y, you know that mQ = mY = 95°. 7

Given STU  YXZ, list all corresponding congruent parts. Checkpoint Name Corresponding Parts and Congruent Triangles Given STU  YXZ, list all corresponding congruent parts. ANSWER T  X; U  Z ST  YX; TU  XZ; SU  YZ; S  Y;

Which congruence statement is correct? Why? Checkpoint Name Corresponding Parts and Congruent Triangles Which congruence statement is correct? Why? A. JKL  MNP B. JKL  NMP C. JKL  NPM ANSWER B; This statement matches up the corresponding vertices in order.

Use the two triangles at the right. Example 4 Determine Whether Triangles are Congruent Use the two triangles at the right. a. Identify all corresponding congruent parts. E D F G SOLUTION a. Corresponding Angles D  G Corresponding Sides DE  GE DEF  GEF DF  GF DFE  GFE EF  EF 10

Since, HJ  KJ, HG  KL, and JG  JL. (marked) So, HJG  KJL. Example 5 Determine Whether Triangles are Congruent In the figure, HG || LK. Determine whether the triangles are congruent. If so, write a congruence statement. SOLUTION HJG  KJL Vertical angles are congruent. H  K Alternate Interior Angles Theorem G  L Alternate Interior Angles Theorem Since, HJ  KJ, HG  KL, and JG  JL. (marked) So, HJG  KJL. 11

yes; Sample answer: XVY  ZVW Checkpoint Determine Whether Triangles are Congruent 4. In the figure, XY || ZW. Determine whether the two triangles are congruent. If they are, write a congruence statement. ANSWER yes; Sample answer: XVY  ZVW

Review

1. Name the smallest and largest angles of the triangle. ANSWER

Name the shortest and longest sides of the triangle. 2. ANSWER 3. ANSWER

Everett noticed that three streets in his town form a triangle Everett noticed that three streets in his town form a triangle. He measured each distance and made this diagram. Are his measurements correct? Explain why or why not. 4. ANSWER

Homework