Question

triangle congruence: sas
quiz complete
1 2 3
the proof that △mns ≅ △qns is shown. select the answer that best completes the proof.
given △mnq is isosceles with base (overline{mq}), and (overline{nr}) and (overline{mq}) bisect each other at s
prove △mns ≅ △qns
we know that △mnq is isosceles with base (overline{mq}). so, (overline{mn}congoverline{qn}) by the definition of isosceles triangle. the base angles of the isosceles triangle, ∠mns and ∠nqs, are congruent by the isosceles triangle theorem. it is also given that (overline{nr}) and (overline{mq}) bisect each other at s. segments______are therefore congruent by the definition of bisector. thus, △mns ≅ △qns by sas
ns and qs
ns and rs
ms and rs
ms and qs

Explanation:

Step1: Comprender la definición de bisectriz

Si dos segmentos se bisecan entre sí, los segmentos resultantes son congruentes. Aquí, \(\overline{NR}\) y \(\overline{MQ}\) se bisecan en \(S\). Esto significa que \(S\) es el punto medio de \(\overline{MQ}\).

Step2: Aplicar la definición de bisectriz a \(\overline{MQ}\)

Por la definición de bisectriz, si \(S\) es el punto medio de \(\overline{MQ}\), entonces \(MS = SQ\), es decir, \(\overline{MS}\cong\overline{QS}\)

Answer:

MS and QS