Five-Minute Check (over Lesson 4–3) Mathematical Practices 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 Lesson Menu

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. SAS C. not possible 5-Minute Check 1

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. SAS C. not possible 5-Minute Check 2

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. SAS C. not possible 5-Minute Check 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. SAS C. not possible 5-Minute Check 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. SAS C. not possible 5-Minute Check 5

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

Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. Content Standards G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. MP

G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. MP

You proved triangles congruent using SSS and SAS. Use the ASA congruence criterion to prove triangles congruent. Use the AAS congruence criterion to prove triangles congruent. Then/Now

included side New Vocabulary

Postulate

Write a two-column proof. Given: Use ASA to Prove Triangles Congruent Write a two-column proof. Given: Prove: WRL ≅ EDL Example 1

Use ASA to Prove Triangles Congruent WR ǁ ED, L is the midpoint of WE Write the given statements. Why is WL ≅ LE? The Midpoint Theorem. Why is  W ≅  E? Alternate Interior Angles Theorem. Why is  WLR ≅  ELD? Vertical Angles Theorem. Why is ∆WRL ≅ ∆EDL? ASA Use the information to write a two-column proof. Example 1

Use ASA to Prove Triangles Congruent Answer: Example 1

Theorem

Write a paragraph proof. Given: NKL ≅ NJM Use AAS to Prove Triangles Congruent Write a paragraph proof. Given: NKL ≅ NJM Prove: Example 2

Use AAS to Prove Triangles Congruent KL ≅ JM,  NKL ≅  NJM Write the given statements. Why is  N ≅  N? The Reflexive Property. Why is ∆ JNM ≅ ∆ KNL? AAS Why is LN ≅ MN CPCTC Use the information to write a paragraph proof. Example 2

Use AAS to Prove Triangles Congruent Answer: Example 2

Apply Triangle Congruence MANUFACTURING Barbara 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 centimeters and the height of the isosceles triangle is 3 centimeters, find PO. Real-World Example 3

Answer: PO = 5 cm Apply Triangle Congruence EV≅ PL , The height of ∆ POL = 3 and is the midpoint of PL Write the given statements. 1 2 PL = 4 The Midpoint Theorem. 42 + 32 = (PO)2 Use the Pythagorean Theorem to find PO. PO = 5 Answer: PO = 5 cm Real-World Example 3