Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4–4) Then/Now New Vocabulary Postulate 4.3: Angle-Side-Angle (ASA) Congruence Example 1:Use.

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Presentation transcript:

Splash Screen

Lesson Menu Five-Minute Check (over Lesson 4–4) 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

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

Over Lesson 4–4 A.A B.B C.C D.D 5-Minute Check 2 A.SSS B.ASA C.SAS D.not possible Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4 A.A B.B C.C D.D 5-Minute Check 3 A.SAS B.AAS C.SSS D.not possible Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

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

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

Over Lesson 4–4 A.A B.B C.C D.D 5-Minute Check 6 Given  A   R, what sides must you know to be congruent to prove ΔABC  ΔRST by SAS? A. B. C. D.

Then/Now You proved triangles congruent using SSS and SAS. (Lesson 4–4) Use the ASA Postulate to test for congruence. Use the AAS Theorem to test for congruence.

Vocabulary included side

Concept

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

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

A.A B.B Example 1 Write a 2-column proof.

Concept

Example 2 Use AAS to Prove Triangles Congruent Write a 2-column proof.

A.A B.B C.C D.D Example 2 A.SSSB. SAS C.ASAD. AAS Complete the following flow proof.

A.A B.B C.C D.D Example 3 A.SSS B.SAS C.ASA D.AAS 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?

Concept

End of the Lesson