Question

Which of the following pairs of triangles can be proven congruent through SAS?

Answer 1

a.

Explanation:

The SAS (Side-Angle-Side) Congruence Theorem states that if two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.

The included angle in a triangle refers to the angle formed by two sides of the triangle that meet at a common vertex.

Therefore, pair "a" is the only set of triangles that demonstrates congruency of two sides and the included angle. In triangles ABC and TUV, side AB is congruent to side TU, side BC is congruent to side UV, and the included angle B is congruent to the included angle U.

Answer 2

We need to find which of the given pairs of triangles can be proved congruent by SAS congruence condition.

SAS is used when the angle and the two sides enclosing the angle of one triangle is congruent to the other triangle .

On looking at the options we can clearly see that this condition is followed in the first option itself.

• In option a AB = TU and BC = UV . These sides enclose the angles ang.ABC and ang.TUV which are also equal.

Hence by SAS the pair of ∆s given in option a are congruent.

and we are done!