Question

which reason is missing from the proof?

1. q is the midpoint of (overline{pr}).

r is the midpoint of (overline{qs}).

1. (overline{pq}congoverline{qr};overline{qr}congoverline{rs})
2. (overline{pq}congoverline{rs})

(a) definition of congruence
(b) reflexive property of congruence
(c) symmetric property of congruence
(d) transitive property of congruence

Explanation:

Step1: Recall properties of congruence

The transitive property of congruence states that if \(a\cong b\) and \(b\cong c\), then \(a\cong c\).

Step2: Apply to the problem

Here, we have \(\overline{PQ}\cong\overline{QR}\) (from step 2) and \(\overline{QR}\cong\overline{RS}\) (from step 2). By the transitive property of congruence, if \(A\cong B\) and \(B\cong C\), then \(A\cong C\). Substituting \(A = \overline{PQ}\), \(B=\overline{QR}\), and \(C = \overline{RS}\), we get \(\overline{PQ}\cong\overline{RS}\).

Answer:

D. Transitive Property of Congruence