The proof that ΔMNS ≅ ΔQNS is shown. 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 bisect each other at S. Segments_____are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.
NS and NS
NS and RS
MS and RS
MS and QS
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.
NS and NS
NS and RS
MS and RS
MS and QS
2 answers:
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