Question

given: q is the midpoint of pr and k is the midpoint of qs.
prove: \overline{pq} \cong \overline{rs}
which reason is missing from the proof?

1. q is the midpoint of \overline{pr}.

r is the midpoint of \overline{qs}.

1. given
2. \overline{pq} \cong \overline{qr}; \overline{qr} \cong \overline{rs}
3. definition of midpoint
4. \overline{pq} \cong \overline{rs}

3.
a) definition of congruence
b) reflexive property of congruence
c) symmetric property of congruence
d) transitive property of congruence

Explanation:

• The transitive property of congruence states that if \(a\cong b\) and \(b\cong c\), then \(a\cong c\).
• In this proof, since \(\overline{PQ}\cong\overline{QR}\) (from \(Q\) being the mid - point of \(\overline{PR}\)) and \(\overline{QR}\cong\overline{RS}\) (from \(R\) being the mid - point of \(\overline{QS}\)), by the transitive property of congruence, we can conclude that \(\overline{PQ}\cong\overline{RS}\).

Answer:

D. Transitive Property of Congruence