Question

let the parallelogram be $pqrs$, labeled circularly. draw diagonal $\overline{pr}LXB0\angle pqr \cong \angle rsp$repeat this reasoning with diagonal $\overline{qs}$ to prove $\angle qps \cong \angle srq$options:asa$\overline{ps} \cong \overline{rq}$; $\overline{qp} \cong \overline{sr}$$\overline{pr} \cong \overline{rp}$alternate interior angles theoremsymmetric property of congruencecpctc$\angle qpr \cong \angle srp$ ; $\angle qrp \cong \angle spr$

Explanation:

Step1: Identify reflexive side

$\overline{PR} \cong \overline{RP}$

Step2: Mark alternate interior angles

By Alternate Interior Angles Theorem:
$\angle QPR \cong \angle SRP$, $\angle QRP \cong \angle SPR$

Step3: Prove triangle congruence

By ASA:
$\triangle QPR \cong \triangle SRP$

Step4: Corresponding angles congruence

By CPCTC:
$\angle PQR \cong \angle RSP$

Step5: Match parallel side congruence

$\overline{PQ} \cong \overline{RS}$, $\overline{QR} \cong \overline{SP}$

Answer:

1. First two top boxes (parallel side congruence): $\boldsymbol{\overline{PQ} \cong \overline{RS}}$, $\boldsymbol{\overline{QR} \cong \overline{SP}}$
2. Next two boxes (angle congruence): $\boldsymbol{\angle QPR \cong \angle SRP}$, $\boldsymbol{\angle QRP \cong \angle SPR}$ (justification: $\boldsymbol{\text{Alternate Interior Angles Theorem}}$)
3. Box for $\triangle QPR \cong \triangle SRP$: $\boldsymbol{\text{ASA}}$
4. Box for $\angle PQR \cong \angle RSP$: $\boldsymbol{\text{CPCTC}}$
5. Reflexive side box: $\boldsymbol{\overline{PR} \cong \overline{RP}}$ (justification: $\boldsymbol{\text{Symmetric Property of Congruence}}$)