Question

given: △hjl≅△klj prove: hjkl is a parallelogram move expressions and phrases into the boxes to complete the proof. statement reason △hjl≅△klj given congruent parts of congruent triangles are congruent quadrilateral hjkl is a parallelogram $overline{hj}congoverline{kl}$ $overline{hl}congoverline{kj}$ $angle hcongangle k$ $angle hljcongangle kjl$ $angle hjlcongangle klj$ alternate interior angles are congruent congruent parts of congruent triangles are congruent if both pairs of opposite sides of a quadrilateral are congruent then it is a parallelogram. if both pairs of opposite angles of a quadrilateral are congruent then it is a parallelogram.

Explanation:

Step1: Identify congruent sides

Since $\triangle HJL\cong\triangle KLJ$, by the property of "Congruent Parts of Congruent Triangles are Congruent", we have $\overline{HJ}\cong\overline{KL}$ and $\overline{HL}\cong\overline{KJ}$.

Step2: Apply parallelogram - side criterion

We know that if both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram. In quadrilateral $HJKL$, $\overline{HJ}$ and $\overline{KL}$ are opposite sides, and $\overline{HL}$ and $\overline{KJ}$ are opposite sides. Since $\overline{HJ}\cong\overline{KL}$ and $\overline{HL}\cong\overline{KJ}$, quadrilateral $HJKL$ is a parallelogram.

Answer:

Statement	Reason
$\overline{HJ}\cong\overline{KL},\overline{HL}\cong\overline{KJ}$	Congruent Parts of Congruent Triangles are Congruent
Quadrilateral $HJKL$ is a parallelogram	If both pairs of opposite sides of a quadrilateral are congruent then it is a parallelogram