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Presentation transcript:

Class Greeting

Objective: The students will be able to Prove Congruence – ASA and AAS.

Proving Congruence – ASA, AAS, and HL Chapter 4 – Lesson 4 Proving Congruence – ASA, AAS, and HL

Given angles G and  C, side CG is the included side Vocabulary Included side (between 2 given angles) The included side between 2 given angles of a triangle is the side that is a common side to both given angles Given angles G and  C, side CG is the included side

Postulate 4.3 ASA (angle-side-angle congruence) If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle then triangles are congruent.

Write a paragraph proof. Given: Prove: WRL EDL ; L is the midpoint of Proof: Since it is given that , because alternate interior angles are congruent. It is also given that L is the midpoint of so by the Midpoint Theorem. Since vertical angles are congruent, Therefore WRL EDL by ASA. Example 5-1a

Theorem 4.5 (AAS) (angle-angle-side congruence) If two angles and a nonincluded side of a triangle are congruent to the corresponding angles and side of a second triangle then the triangles are congruent

Write a flow proof. Given: Prove: Proof: Example 5-2a

Given: Prove: Write a flow proof. Proof: Example 5-2c

Kahoot!

Lesson Summary: Objective: The students will be able to Prove Congruence – ASA and AAS.

Preview of the Next Lesson: Objective: The students will be able to Prove Right Triangle Congruence – LL, HA, LA and HL.

Stand Up Please