Proving Triangles Congruent – ASA, AAS LESSON 4–5 Proving Triangles Congruent – ASA, AAS

Five-Minute Check (over Lesson 4–4) TEKS 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 Proof: Angle-Angle-Side Theorem Example 2: Use AAS to Prove Triangles Congruent Example 3: Real-World Example: Apply Triangle Congruence Concept Summary: Proving Triangles Congruent 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. ASA C. SAS D. 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. ASA C. SAS D. 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. SAS B. AAS C. SSS D. 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. SSA B. ASA C. SSS D. 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. AAA B. SAS C. SSS D. 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 Processes G.1(B), Also addresses G.1(G) Targeted TEKS G.6(B) Prove two triangles are congruent by applying the Side-Angle-Side, Angle-Side-Angle, Side-Side-Side, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions. G.6(D) Verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, mid-segments, and medians, and apply these relationships to solve problems. Also addresses G.5(C). Mathematical Processes G.1(B), Also addresses G.1(G) TEKS

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

included side Vocabulary

Concept

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

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

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

Theorem

Proof

Write a paragraph proof. Use AAS to Prove Triangles Congruent 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. __ ___ Example 2

Complete the following flow proof. A. SSS B. SAS C. ASA D. AAS 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 cm and the height of the isosceles triangle is 3 cm, find PO. Example 3

NV  EN by definition of isosceles triangle Apply Triangle Congruence In order to determine the length of PO, we must first prove that the two triangles are congruent. ____ ΔENV  ΔPOL by ASA. NV  EN by definition of isosceles triangle ____ EN  PO by CPCTC. ____ NV  PO by the Transitive Property of Congruence. ____ 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

The curtain decorating the window forms 2 triangles at the top 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

Concept

Proving Triangles Congruent – ASA, AAS LESSON 4–5 Proving Triangles Congruent – ASA, AAS