Question

Given that ZQ is congruent to ZR and that PQ is congruent to PR, show that PV = P7?

A. ZP: ZP by the reflexive property of congruence, so APQV = APRT by ASA. Therefore,
PV PT by CPCTC.
B. ZP: ZP by the reflexive property of congruence, so AQTW=ARTW by ASA. Therefore,
PV = PT by CPCTC.
C. ZRTP = ZQVP by the transitive property of congruence, so APQV=APRI by AAS. Therefore,
PV PT by CPCTC.
D. ZP: ZP by the symmetric property of congruence, so APQV = APRT by SAS. Therefore,
PVPT by CPCTC.

Answer 1

Using the reflexive property of congruence and the ASA congruence theorem, we showed that triangle APQV is congruent to APRT, which concludes that PV is equal to PT by the CPCTC theorem.

Step-by-step explanation:

To prove that PV = PT, we must show that triangle PQV is congruent to triangle PRT. Given that angle ZQ is congruent to angle ZR and PQ is congruent to PR, we also know ZP is congruent to ZP (itself) by the reflexive property of congruence. With these given, we can apply the Angle-Side-Angle (ASA) congruence theorem to show that triangle APQV is congruent to triangle APRT, as they share two angles and a side in common.

By the Congruent Parts of Congruent Triangles are Congruent (CPCTC) theorem, corresponding parts of these congruent triangles, namely PV and PT, must also be congruent. This deduction aligns with option (A) in our given choices.