Question

The proof that is shown. Select the answer that best completes the proof.

Given: ΔMNQ is isosceles with base , and and bisect each other at S.
Prove:

Square M N Q R is shown with point S in the middle. Lines are drawn from each point of the square to point S to form 4 triangles.

We know that ΔMNQ is isosceles with base . So, by the definition of isosceles triangle. The base angles of the isosceles triangle, and , are congruent by the isosceles triangle theorem. It is also given that and bisect each other at S. Segments _______ are therefore congruent by the definition of bisector. Thus, by SAS.

NS and QS
NS and RS
MS and RS
MS and QS

Answer 1

MS and QS

Since the diagonals bisect each other at S, MS = SQ. With MN = NQ (sides of the square) and ∠SMN = ∠SQN (the base angles of isosceles ΔMNQ), triangles SMN and SQN are congruent by SAS.