# Triangle Congruence Cases

- Author:
- Jorge Cássio

- Topic:
- Angles, Congruence, Triangles

## 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?

## 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'.