Question

ngruence: sas
which rigid transformation would map △aqr to △akp?
a rotation about point a
a reflection across the line
containing aq
a rotation about point r
a reflection across the line
containing ar

Explanation:

Step1: Analyze rotation about point \(A\)

When we rotate \(\triangle AQR\) about point \(A\), we can observe that the lengths \(AQ = AK\) (marked as equal), \(AR = AP\) (marked as equal) and the included angles \(\angle QAR=\angle KAP\) (given congruence by \(SAS\)). A rotation about point \(A\) will map \(Q\) to \(K\) and \(R\) to \(P\) since the distances from \(A\) (i.e., \(AQ = AK\) and \(AR = AP\)) and the angle between them are preserved.

Step2: Analyze other options

• A reflection across the line containing \(AQ\): This would not map \(R\) to \(P\) as the orientation and position relative to \(AQ\) would not match the congruence \(SAS\) for \(\triangle AQR\) and \(\triangle AKP\).
• A rotation about point \(R\): Point \(R\) is a vertex of \(\triangle AQR\). Rotating about \(R\) would not align the sides \(AQ\) and \(AK\) (since \(AQ\) is not fixed at \(R\)) as required by the \(SAS\) congruence.
• A reflection across the line containing \(AR\): This would not map \(Q\) to \(K\) in a way that satisfies the \(SAS\) congruence for \(\triangle AQR\) and \(\triangle AKP\)

Answer:

a rotation about point \(A\)