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Triangle Congruence: Angle-Side-Angle & Angle-Angle-Side ASA & AAS

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Presentation on theme: "Triangle Congruence: Angle-Side-Angle & Angle-Angle-Side ASA & AAS"β€” Presentation transcript:

1 Triangle Congruence: Angle-Side-Angle & Angle-Angle-Side ASA & AAS
Lesson 30 Triangle Congruence: Angle-Side-Angle & Angle-Angle-Side ASA & AAS

2 Review Vocabulary The angle formed by two adjacent sides of a polygon is called an included angle. What is the included angle of 𝐴𝐷 & 𝐴𝐡 ? ∠A The common side of two consecutive angles of a polygon is called an included side. What is the included side of ∠D & ∠C? 𝐷𝐢

3 Postulate 16: -Angle-Side-Angle (ASA) Triangle Congruence Postulate
If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent. Ξ”KGB β‰… Ξ”CIA, ASA

4 Find the value of y ∠FMH & ∠JML are vertical angles so they are congruent. Therefore Ξ”HMF β‰… Ξ”JML, ASA By CPCTC 𝐹𝐻 β‰… 𝐿𝐽 2π‘¦βˆ’5=63 2𝑦=68 𝑦=34

5 What can you conclude about ∠G and ∠I?
Hint: Corollary (No Choice Thm) ∠G β‰… ∠I Now what can you conclude about the 2 triangles? They are congruent by ASA This leads us to our next theorem and 4th triangle congruence

6 Theorem 30-1: Angle-Angle-Side (AAS)
If 2 angles and the nonincluded side of one triangle are congruent to 2 angles and the nonincluded side of another triangle, then the triangles are congruent. Ξ”KGB β‰… Ξ”CIA, AAS

7 GIVEN: ∠𝐿 β‰…βˆ π‘ 𝑀𝑃 𝑏𝑖𝑠𝑒𝑐𝑑𝑠 βˆ πΏπ‘€π‘ PROVE: Ξ”MPL β‰… Ξ”MPN
Statements Reasons ∠𝐿 β‰…βˆ π‘ 𝑀𝑃 𝑏𝑖𝑠𝑒𝑐𝑑𝑠 βˆ πΏπ‘€π‘ βˆ πΏπ‘€π‘ƒ β‰…βˆ π‘π‘€π‘ƒ 𝑀𝑃 β‰… 𝑀𝑃 Ξ”MPL β‰… Ξ”MPN Given Def. of Angle Bisector Reflexive of β‰… AAS

8 GIVEN: 𝑄𝑇 βŠ₯ 𝑅𝑆 ; 𝑄𝑇 bisects βˆ π‘…π‘„π‘† PROVE: Ξ”RTQ β‰… Ξ”STQ
Statements Reasons 𝑄𝑇 βŠ₯ 𝑅𝑆 βˆ π‘„π‘‡π‘…β‰…βˆ π‘„π‘‡π‘† 𝑄𝑇 bisects βˆ π‘…π‘„π‘† βˆ π‘‡π‘„π‘…β‰…βˆ π‘‡π‘„π‘† 𝑄𝑇 β‰… 𝑄𝑇 Ξ”RTQ β‰… Ξ”STQ Given Thm 5-4 (βŠ₯ lines, form β‰… βˆ β€™s) Def. of Angle Bisector Reflexive of β‰… ASA

9 Conclusion Proving triangles will prepare you for :
Lesson 38: Perpendicular and Angle Bisectors of Triangles Lesson 46: Triangle Similarity Lesson 51: Properties of Isosceles and Equilateral Triangles Lesson 55: Triangle Midsegment Thm

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