[Answer] We know that ΔMNQ is isosceles with base MQ. So MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle ∠NMS and ∠NQS are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments ___ are therefore congruent by the definition of bisector. Thus ΔMNS ≅ ΔQNS by SAS.

Answer: D

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We know that ΔMNQ is isosceles with base MQ. So MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle ∠NMS and ∠NQS are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments ___ are therefore congruent by the definition of bisector. Thus ΔMNS ≅ ΔQNS by SAS. We know that ΔMNQ is isosceles with base MQ . So MN ≅ QN by the definition of isosceles triangle . The base angles of the isosceles triangle ∠ NMS and ∠NQS are congruent by the isosceles triangle theorem . It is also given that NR and MQ bisect each other at S . Segments ___ are therefore congruent by the definition of bisector . We know that ΔMNQ is isosceles with base MQ . So MN ≅ QN by the definition of isosceles triangle . The base angles of the isosceles triangle ∠ NMS and ∠NQS are congruent by the isosceles triangle theorem . ... It is also given that NR and MQ bisect each other at S . Segments _____ are therefore congruent by the definition of bisector . Thus ... Given: ΔMNQ is isosceles with base MQ and NR and MQ bisect each other at S . Prove: ΔMNS ≅ ΔQNS We know that ΔMNQ is isosceles with base MQ . So MN ≅ QN by the definition of isosceles triangle . The base angles of the isosceles triangle ∠ NMS and ∠NQS are congruent by the isosceles triangle theorem . It is also given that NR and MQ ... So segment MN is congruent or equal to segment QN by the definition of isosceles triangle . The base angles of the isosceles triangle NMS and NQS are congruent by the isosceles triangle theorem . It is also given that segment NR and segment MQ bisect each other at S . Segments ______________ are therefore congruent by the definition of bisector . So MN ≅ QN by the definition of isosceles triangle . The base angles of the isosceles tr...

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