Question

use the properties of rigid motions to complete the proof. given: pq¯≅qr¯ and m∠pqs≅m∠rqs prove: qs¯⊥pr¯ and ps¯≅sr¯ reflect △qps across qs¯. reflections preserve angle measures and distances, so the image of qp¯ lies along and has the same length as

Explanation:

Step1: Recall reflection property

A reflection across a line (in this case QS) preserves distances. Given that we are reflecting △QPS across QS, the image of a segment will have the same length as the original segment. Since we know that PQ≅QR and PS≅SR and we are reflecting △QPS across QS, the image of QP will lie along QR and have the same length as QR because of the properties of reflection (rigid - motion) which preserve lengths.

Answer:

QR