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Warm Up on desk

Test your knowledge on identifying congruent triangles and their corresponding parts. Learn the vocabulary and practice solving examples.

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Warm Up on desk

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  1. Warm Upon desk • Do the Daily Quiz

  2. 5.1 • ESSENTIAL QUESTION • How do you identify congruent triangles and its corresponding parts?

  3. 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.

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

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

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

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

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

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

  10. Example 5 Determine Whether Triangles are Congruent Inthe 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. Checkpoint yes; Sample answer: XVY ZVW ANSWER Determine Whether Triangles are Congruent 4. Inthe figure, XY ||ZW. Determine whether the two triangles are congruent. If they are, write a congruence statement.

  12. Review

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

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

  15. 4. 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. ANSWER

  16. Homework

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