Valid Congruence Tests for Triangles: Don’t Rely on SSA – Learn SAS, SSS, ASA, and AAS Here!

These triangles are not necessarily congruent because SSA (side-side-angle) is not a valid test!

Corresponding Parts of Corresponding Triangle are Congruent; Can be used in a proof of triangle congruence

You are correct that SSA (side-side-angle) is not a valid test for proving the congruence of triangles. This is because two triangles can have the same side lengths and the same angle measurements, but different shapes.

To prove that two triangles are congruent, we should use one of the valid congruence tests such as:

1. SAS (side-angle-side): If two sides and the included angle of a triangle are equal to the corresponding sides and included angle of another triangle, then the two triangles are congruent.

2. SSS (side-side-side): If the three sides of a triangle are equal to the corresponding sides of another triangle, then the two triangles are congruent.

3. ASA (angle-side-angle): If two angles and the included side of a triangle are equal to the corresponding angles and included side of another triangle, then the two triangles are congruent.

4. AAS (angle-angle-side): If two angles and a non-included side of a triangle are equal to the corresponding angles and non-included side of another triangle, then the two triangles are congruent.

It’s important to remember that we need at least three pieces of information in order to prove the congruence of triangles. Also, it’s important to use a valid congruence test for the given situation.

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