Chapter 4.5 Notes: Prove Triangles Congruent by ASA and AAS Goal: You will use two more methods to prove congruences.

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Presentation transcript:

Chapter 4.5 Notes: Prove Triangles Congruent by ASA and AAS Goal: You will use two more methods to prove congruences.

An included side is a segment that connects two angles together. An included side is the common leg of two angles. Postulate 21 Angle-Side-Angle (ASA) Congruence Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

Theorem 4.6 Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

Ex.1: Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.

Ex.2: In the diagram below, what postulate or theorem can you use to prove that ? Explain. Ex.3: Complete the proof. Given: Prove:

Ex.4: Complete the proof. Given: Prove:

Ex.5: Complete the proof. Given: Prove: A D B C E F

Ex.6: Complete the proof. Given: Prove: C B D F A E