Question

h is the midpoint of \\(overline{gi}\\), \\(overline{hk} \cong overline{hj}\\), and \\(overline{gj} \cong overline{ik}\\). complete the proof that \\(\triangle ghj \cong \triangle ihk\\).

statement	reason
2 \\(overline{hk} \cong overline{hj}\\)	given
3 \\(overline{gj} \cong overline{ik}\\)	given
4

Explanation:

Step1: Derive congruent segments

Since $H$ is the midpoint of $\overline{GI}$, $\overline{GH} \cong \overline{IH}$ (Definition of midpoint)

Step2: List all congruent sides

We have:

1. $\overline{GH} \cong \overline{IH}$ (From Step1)
2. $\overline{HJ} \cong \overline{HK}$ (Given)
3. $\overline{GJ} \cong \overline{IK}$ (Given)

Step3: Apply SSS congruence rule

By the Side-Side-Side (SSS) Congruence Postulate, if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. So $\triangle GHJ \cong \triangle IHK$

Answer:

$\triangle GHJ \cong \triangle IHK$