Using Side-Angle-Side (SAS) Criteria to Prove Congruence Between Two Triangles

side-angle-side

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

Side-angle-side (SAS) is a criteria used to prove congruence between two triangles. It states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

To use SAS to prove triangles congruent, we must show that both triangles have two sides and the angle between them that are congruent. This tells us that the third side and all the other angles of the two triangles must be congruent as well.

For example, suppose we have Triangle ABC with side AB = 6 cm, side AC = 5 cm, and angle A = 60°. We also have Triangle DEF with side DE = 6 cm, side DF = 5 cm, and angle D = 60°. To prove that these two triangles are congruent using SAS, we need to show that side AB and side DE are congruent, side AC and side DF are congruent, and angle A and angle D are congruent.

Once we have shown that these three parts are congruent, we can conclude that the two triangles are congruent. Therefore, the other sides and angles of both triangles will also be congruent.

Overall, to prove two triangles congruent using SAS, we must show the following:

1. Two sides of one triangle are congruent to two sides of another triangle.
2. The included angle between those two sides is congruent in both triangles.
3. Therefore, the two triangles must be congruent.

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