Question

$overline{hk} cong overline{ij}$ and $overline{jk} cong overline{hi}$. complete the proof that $\triangle hjk cong \triangle jhi$.

	statement	reason
2	$overline{jk} cong overline{hi}$
3	$overline{hj} cong overline{hj}$
4	$\triangle hjk cong \triangle jhi$

Explanation:

Step1: Identify given statement 1

Reason: Given (matches the problem's first given: $\overline{HK} \cong \overline{IJ}$)

Step2: Identify given statement 2

Reason: Given (matches the problem's second given: $\overline{JK} \cong \overline{HI}$)

Step3: Justify shared side congruence

Reason: Reflexive Property of Congruence (a segment is congruent to itself: $\overline{HJ} \cong \overline{HJ}$)

Step4: Prove triangle congruence

Reason: Side-Side-Side (SSS) Congruence Postulate (all three pairs of corresponding sides are congruent, so $\triangle HJK \cong \triangle JHI$)

Answer:

1. Given
2. Given
3. Reflexive Property of Congruence
4. Side-Side-Side (SSS) Congruence Postulate