h is the midpoint of $\overline{gi}$. complete the proof that $\triangle ghj \cong \triangle ihk$.
| statement | reason |
| --- | --- |
| 1 $h$ is the midpoint of $\overline{gi}$ | given |
| 2 $\overline{gj} \cong \overline{ik}$ | given |
| 3 $\overline{hj} \cong \overline{hk}$ | given |
| 4 $\overline{gh} \cong \overline{hi}$ | definition of midpoint |
| 5 $\triangle ghj \cong \triangle ihk$ | |

Question

h is the midpoint of $\overline{gi}$. complete the proof that $\triangle ghj \cong \triangle ihk$.
| statement | reason |
| --- | --- |
| 1 $h$ is the midpoint of $\overline{gi}$ | given |
| 2 $\overline{gj} \cong \overline{ik}$ | given |
| 3 $\overline{hj} \cong \overline{hk}$ | given |
| 4 $\overline{gh} \cong \overline{hi}$ | definition of midpoint |
| 5 $\triangle ghj \cong \triangle ihk$ |  |

Accepted Answer

# Explanation:
## Step1: Identify Congruent Parts
We have $ \overline{GJ} \cong \overline{IK} $ (given), $ \overline{HJ} \cong \overline{HK} $ (given), and $ \overline{GH} \cong \overline{HI} $ (from midpoint, so $ GH = HI $).
## Step2: Apply SSS Congruence
By the Side - Side - Side (SSS) Congruence Postulate, if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. For $ \triangle GHJ $ and $ \triangle IHK $, we have $ \overline{GJ} \cong \overline{IK} $, $ \overline{HJ} \cong \overline{HK} $, and $ \overline{GH} \cong \overline{HI} $. So the reason for $ \triangle GHJ \cong \triangle IHK $ is the SSS Congruence Postulate.
# Answer:
SSS Congruence Postulate

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QUESTION IMAGE

Question

Explanation:

Step1: Identify Congruent Parts

Step2: Apply SSS Congruence

Answer:

statement	reason
2 \\(\overline{gj} \cong \overline{ik}\\)	given
3 \\(\overline{hj} \cong \overline{hk}\\)	given
4 \\(\overline{gh} \cong \overline{hi}\\)	definition of midpoint
5 \\(\triangle ghj \cong \triangle ihk\\)