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The proof that \( \triangle M N S \cong \triangle Q N S \) is shown. We know that \( \triangle \mathrm{MNQ} \) is isosceles with base \( \overline{\mathrm{MQ}} \). So, Given: \( \triangle M N Q \) is isosceles with base \( \overline{M Q}, \bar{a}, \overline{N R} \) and \( \quad \overline{M N} \cong \overline{Q N} \) by the definition of isosceles triangle. The \( \overline{\mathrm{MQ}} \) bisect each other at \( \mathrm{S} \). base angles of the isosceles triangle, \( \angle \mathrm{NMS} \) and \( \angle \mathrm{NQS} \), Prove: \( \triangle M N S \cong \triangle Q N S \quad \) are congruent by the isosceles triangle theorem. It is also given that \( \overline{N R} \) and \( \overline{M Q} \) bisect each other at \( S \).

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