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'.