Question

given:
qrs is an isosceles △.
if m is midpoint of rq, what conclusion can be drawn about the two smaller triangles?
△sqm ≅ △mrs
△sqm ≅ △smr
△smq ≅ △srm
△sqm ≅ △srm

Explanation:

Step1: Analyze the properties of isosceles triangle

Since \( \triangle QRS\) is isosceles, \(SQ = SR\).

Step2: Use the mid - point property

Given \(M\) is the mid - point of \(RQ\), so \(QM=RM\).

Step3: Check the congruence condition

In \( \triangle SQM\) and \( \triangle SRM\), \(SQ = SR\) (sides of isosceles triangle), \(QM = RM\) (mid - point), and \(SM\) is common side. By SSS (Side - Side - Side) congruence criterion, \( \triangle SQM\cong\triangle SRM\).

Answer:

\(\triangle SQM\cong\triangle SRM\)