Question

given : qr ≅ rs and ∠qrt ≅ ∠srt
prove : △qrt ≅ △srt
qr ≅ rs
given
rt ≅ rt
∠qrt ≅ ∠srt

Explanation:

Step1: Analyze the given information

We are given \( QR\cong RS\) (side) and \(\angle QRT\cong\angle SRT\) (angle). Also, \(RT\cong RT\) by the Reflexive Property of Congruence (common side).

Step2: Apply the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle QRT\) and \(\triangle SRT\), we have:

• \(QR = RS\) (given)
• \(\angle QRT=\angle SRT\) (given)
• \(RT = RT\) (common side, Reflexive Property)

So, by the SAS congruence criterion, \(\triangle QRT\cong\triangle SRT\)

Answer:

\(\triangle QRT\cong\triangle SRT\) by the SAS (Side - Angle - Side) congruence criterion.