k is the midpoint of $\overline{hj}$ and $\overline{gi}$. complete the proof that $\triangle gjk \cong \triangle ihk$.

| statement | reason |
| --- | --- |
| 1 $k$ is the midpoint of $\overline{hj}$ | given |
| 2 $k$ is the midpoint of $\overline{gi}$ | given |
| 3 $\overline{hk} \cong \overline{jk}$ | definition of midpoint |
| 4 $\overline{gk} \cong \overline{ik}$ | definition of midpoint |
| 5 | |

Question

k is the midpoint of $\overline{hj}$ and $\overline{gi}$. complete the proof that $\triangle gjk \cong \triangle ihk$.

| statement | reason |
| --- | --- |
| 1 $k$ is the midpoint of $\overline{hj}$ | given |
| 2 $k$ is the midpoint of $\overline{gi}$ | given |
| 3 $\overline{hk} \cong \overline{jk}$ | definition of midpoint |
| 4 $\overline{gk} \cong \overline{ik}$ | definition of midpoint |
| 5 |  |

Accepted Answer

# Answer:
Statement 5: $\angle GKJ \cong \angle IHK$
Reason 5: Vertical Angles Theorem
Statement 6: $	riangle GJK \cong 	riangle IHK$
Reason 6: SAS Congruence Postulate

# Explanation:
## Step1: Identify vertical angles
Vertical angles formed by intersecting segments $\overline{HJ}$ and $\overline{GI}$ at $K$ are congruent.
$\angle GKJ \cong \angle IKH$
## Step2: Apply SAS congruence
We have two pairs of congruent sides ($\overline{HK} \cong \overline{JK}$, $\overline{GK} \cong \overline{IK}$) and the included congruent vertical angles. By the Side-Angle-Side (SAS) Congruence Postulate, the triangles are congruent.
$	riangle GJK \cong 	riangle IHK$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify vertical angles

Step2: Apply SAS congruence

Answer:

statement	reason
2 \\(k\\) is the midpoint of \\(\overline{gi}\\)	given
3 \\(\overline{hk} \cong \overline{jk}\\)	definition of midpoint
4 \\(\overline{gk} \cong \overline{ik}\\)	definition of midpoint
5