Angle-Angle-Side (AAS): Quick Exploration

Below, we have two triangles. All we know here is [b]2 angles and a non-included side of one triangle[/b] are congruent to[b] 2 angles and a non-included side of the other triangle[/b].

Test to see if these two triangles are congruent by trying to place one on top of the other. Note: LARGE POINTS are moveable. The slider (lower right) controls one of the angle measures.

Are the triangles above congruent?

No Yes

If you answered YES to the question above, which rigid transformations did you use to superimpose one triangle on top of the other?

Rotation around point Translation by vector Reflection about line

Interact with the app below for a few minutes. Then answer the question that follows.

The [b]Angle-Angle-Side Triangle Congruence Theorem[/b] should be no surprise to us. Which other triangle congruence theorem is disguised here?

SSS Triangle Congruence Theorem SAS Triangle Congruence Theorem ASA Triangle Congruence Theorem

If 2 angles of one triangle are congruent to 2 angles of another triangle, what can we conclude about the 3rd pair of angles?

Why can we make this conclusion?

Angle-Angle-Side (AAS): Quick Exploration

Test to see if these two triangles are congruent by trying to place one on top of the other. Note: LARGE POINTS are moveable. The slider (lower right) controls one of the angle measures.

Interact with the app below for a few minutes. Then answer the question that follows.

Information: Angle-Angle-Side (AAS): Quick Exploration