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Triangle Congruence Postulates and Examples

Learn how to use the ASA and AAS postulates to prove triangle congruence. Includes examples and real-world applications.

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Triangle Congruence Postulates and Examples

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 4–4) CCSS Then/Now New Vocabulary Postulate 4.3: Angle-Side-Angle (ASA) Congruence Example 1: Use ASA to Prove Triangles Congruent Theorem 4.5: Angle-Angle-Side (AAS) Congruence Example 2: Use AAS to Prove Triangles Congruent Example 3: Real-World Example: Apply Triangle Congruence Concept Summary: Proving Triangles Congruent Lesson Menu

  3. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SSS B. ASA C. SAS D. not possible 5-Minute Check 1

  4. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SSS B. ASA C. SAS D. not possible 5-Minute Check 1

  5. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SSS B. ASA C. SAS D. not possible 5-Minute Check 2

  6. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SSS B. ASA C. SAS D. not possible 5-Minute Check 2

  7. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SAS B. AAS C. SSS D. not possible 5-Minute Check 3

  8. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SAS B. AAS C. SSS D. not possible 5-Minute Check 3

  9. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SSA B. ASA C. SSS D. not possible 5-Minute Check 4

  10. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. SSA B. ASA C. SSS D. not possible 5-Minute Check 4

  11. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. AAA B. SAS C. SSS D. not possible 5-Minute Check 5

  12. Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible. A. AAA B. SAS C. SSS D. not possible 5-Minute Check 5

  13. A. B. C. D. Given A  R, what sides must you know to be congruent to prove ΔABC  ΔRST by SAS? 5-Minute Check 6

  14. A. B. C. D. Given A  R, what sides must you know to be congruent to prove ΔABC  ΔRST by SAS? 5-Minute Check 6

  15. Content Standards G.CO.10 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 5 Use appropriate tools strategically. CCSS

  16. You proved triangles congruent using SSS and SAS. • Use the ASA Postulate to test for congruence. • Use the AAS Theorem to test for congruence. Then/Now

  17. included side Vocabulary

  18. Concept

  19. Use ASA to Prove Triangles Congruent Write a two-column proof. Example 1

  20. Proof: Statements Reasons 1. L is the midpoint of WE. 1. Given ____ 2. 2. Midpoint Theorem 3. 3. Given 5. WLR  ELD 6. ΔWRL  ΔEDL 4. W  E 4. Alternate Interior Angles 5. Vertical Angles Theorem 6. ASA Use ASA to Prove Triangles Congruent Example 1

  21. Fill in the blank in the following paragraph proof. A. SSS B. SAS C. ASA D. AAS Example 1

  22. Fill in the blank in the following paragraph proof. A. SSS B. SAS C. ASA D. AAS Example 1

  23. Concept

  24. Write a paragraph proof. __ ___ Proof: NKL  NJM, KL  MN, and N  N by the Reflexive property. Therefore, ΔJNMΔKNL by AAS. By CPCTC, LN MN. __ ___ Use AAS to Prove Triangles Congruent Example 2

  25. Complete the following flow proof. A. SSS B. SAS C. ASA D. AAS Example 2

  26. Complete the following flow proof. A. SSS B. SAS C. ASA D. AAS Example 2

  27. Apply Triangle Congruence MANUFACTURINGBarbara designs a paper template for a certain envelope. She designs the top and bottom flaps to be isosceles triangles that have congruent bases and base angles. If EV = 8 cm and the height of the isosceles triangle is 3 cm,find PO. Example 3

  28. ____ In order to determine the length of PO, we must first prove that the two triangles are congruent. ____ ____ • NV EN by definition of isosceles triangle ____ ____ • EN PO by CPCTC. ____ ____ • NV PO by the Transitive Property of Congruence. Apply Triangle Congruence • ΔENV ΔPOL by ASA. Since the height is 3 centimeters, we can use the Pythagorean theorem to calculate PO. The altitude of the triangle connects to the midpoint of the base, so each half is 4. Therefore, the measure of PO is 5 centimeters. Answer: Example 3

  29. ____ In order to determine the length of PO, we must first prove that the two triangles are congruent. ____ ____ • NV EN by definition of isosceles triangle ____ ____ • EN PO by CPCTC. ____ ____ • NV PO by the Transitive Property of Congruence. Apply Triangle Congruence • ΔENV ΔPOL by ASA. Since the height is 3 centimeters, we can use the Pythagorean theorem to calculate PO. The altitude of the triangle connects to the midpoint of the base, so each half is 4. Therefore, the measure of PO is 5 centimeters. Answer:PO = 5 cm Example 3

  30. The curtain decorating the window forms 2 triangles at the top. B is the midpoint of AC. AE = 13 inches and CD = 13 inches. BE and BD each use the same amount of material, 17 inches. Which method would you use to prove ΔABE  ΔCBD? A. SSS B. SAS C. ASA D. AAS Example 3

  31. The curtain decorating the window forms 2 triangles at the top. B is the midpoint of AC. AE = 13 inches and CD = 13 inches. BE and BD each use the same amount of material, 17 inches. Which method would you use to prove ΔABE  ΔCBD? A. SSS B. SAS C. ASA D. AAS Example 3

  32. Concept

  33. End of the Lesson

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