1. 4.4 Proving Triangles are Congruent: ASA and AAS Objectives: - Prove that triangles are congruent using ASA and AAS

2. ASA

• If 2 angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the 2 triangles are congruent.

A B C Q R S

3. AAS

• If 2 angles and a nonincluded side of one triangle are congruent to 2 angles and the corresponding nonincluded side of a second triangle, then the 2 triangles are congruent.

A B C Q R S

4. AAS Proof

• If 2 angles are congruent, so is the 3rd

• Third Angle Theorem

• Now QR is an included side, so ASA.

A B C Q R S

5. Example

• Is it possible to prove these triangles are congruent?

6. Example

• Is it possible to prove these triangles are congruent?

• Yes - vertical angles are congruent, so you have ASA

7. Example

• Is it possible to prove these triangles are congruent?

8. Example

• Is it possible to prove these triangles are congruent?

• No. You can prove an additional side is congruent, but that only gives you SS

9. Example

• Is it possible to prove these triangles are congruent?

1 2 3 4

10. Example

• Is it possible to prove these triangles are congruent?

• Yes. The 2 pairs of parallel sides can be used to show Angle 1 =~ Angle 3 and Angle 2 =~ Angle 4. Because the included side is congruent to itself, you have ASA.

1 2 3 4

11. Meteorite example

• Page 222 describes a meteor sighting. 2 witnesses saw the meteor from different locations and recorded the angle. When you draw these sightlines, you know where to look for the meteor.

• How important is accuracy? If the angles were off by 2 in either direction, the location would lie in a 25 square mile area.

12. Do p. 223 2-13, 28

• Quiz tomorrow

• Homework: worksheets