Question

1. prove that the triangles are congruent or explain why this is not possible.

Explanation:

Step1: Identify the sides of the triangles

In \(\triangle RQT\) and \(\triangle RST\), we have \(RQ = 9m\), \(RS=9m\), \(QT = 6m\), \(ST = 6m\), and \(RT\) is common to both triangles.

Step2: Apply SSS (Side - Side - Side) congruence criterion

The SSS congruence criterion states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
For \(\triangle RQT\) and \(\triangle RST\):

• \(RQ=RS = 9m\)
• \(QT=ST = 6m\)
• \(RT = RT\) (common side)

Answer:

By the SSS (Side - Side - Side) congruence criterion, \(\triangle RQT\cong\triangle RST\) since \(RQ = RS\), \(QT=ST\), and \(RT\) is common.