Triangle Congruence Cases

These are properties that allow us to conclude that two triangles are congruent from just three determined congruences.

2nd Case of Congruence - Angle-Side-Angle

1- Why is the proof strategy correct?

Check all that apply

Proof steps.

2- Move the "Steps" selector and follow the proof steps. Do you understand? If you didn't understand, write what you didn't understand.

3rd Case of Congruence - Side-Side-Side (SSS)

Proof of the 3rd case of congruence

Analysis

Change the position of point C so that you have an obtuse triangle. Do any of the steps in the proof have changed? Which ones?

Exterior angles

In order to understand the proof of the 4th postulate, we need to explore a property of the exterior angle of the triangle. First, we will see what is an exterior angle of a convex polygon.

Exterior angles of the convex polygon.

Exterior Angles of a Triangle

Property of the exterior angle of the triangle

Analysis

Check the box show / hide angle measurements. Change the position of points A, B or C. Compare an exterior angle with its non-adjacent ones. What can you see?

Change the selector "Steps"

Observation

You may have noticed that the exterior angle is equal to the sum of the non-adjacent interior angles. The argument for this property will be discussed in the chapter that deals with parallelism.

4th case of congruence - AAS

Finish the Proof

Prove that AB cannot be greater than A'B'.