Question

if $\triangle gjkcong\triangle rqp$, choose the correct statement from the list below
$angle qcongangle k,angle pcongangle k,$
$overline{kj}congoverline{pr},overline{gj}congoverline{qp}$
choose the correct answer below.
a. $angle pcongangle k$
b. $angle qcongangle k$
c. $overline{kj}congoverline{pr}$
d. $overline{gj}congoverline{qp}$

Explanation:

Step1: Analyze the congruent triangles

When \(\triangle GJK\cong\triangle RQP\), the corresponding parts are equal. That is, \(\angle G\cong\angle R\), \(\angle J\cong\angle Q\), \(\angle K\cong\angle P\), \(\overline{GJ}\cong\overline{RQ}\), \(\overline{JK}\cong\overline{QP}\), \(\overline{GK}\cong\overline{RP}\).

Step2: Check each option

• Option A: Since \(\angle K\cong\angle P\) (from the congruence of \(\triangle GJK\) and \(\triangle RQP\)), \(\angle P\cong\angle K\) is correct.
• Option B: \(\angle J\cong\angle Q

eq\angle K\).

• Option C: \(\overline{JK}\cong\overline{QP}

eq\overline{PR}\).

• Option D: \(\overline{GJ}\cong\overline{RQ}

eq\overline{QP}\).

Answer:

A. \(\angle P\cong\angle K\)