The proof that is shown. 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

ΔMNQ is said to be an isosceles triangle, and a side is bisected at S, based on the definition of bisector, the segments that are congruent are: MS and QS.

What is the Isosceles Triangle Theorem?

According to the isosceles triangle theorem, if two sides of a triangle are said to congruent or equal in length, then, the angles that are opposite to these two congruent sides are also congruent to each other.

Thus, since ΔMNQ is said to be an isosceles triangle, and a side is bisected at S, based on the definition of bisector, the segments that are congruent are: MS and QS.

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