Question

Select one of the triangle theorems and write a proof for it.

Answer 1

Look at the attached picture

Explanation:

Yes, they are congruent by the SAS Theorem

From the figure, we see that there are two congruent pairs of corresponding sides, AC¯¯¯¯¯¯¯¯≅DF¯¯¯¯¯¯¯¯,BC¯¯¯¯¯¯¯¯≅EF¯¯¯¯¯¯¯¯, and one congruent pair of corresponding angles, ∠C≅∠F. The Side-Angle-Side Theorem (SAS) states that if two sides and the angle between those two sides of a triangle are equal to two sides and the angle between those sides of another triangle, then these two triangles are congruent.

Answer 2

When triangles are congruent, one triangle can be moved (through one, or more, rigid motions) to coincide with the other triangle.