Question

$\overline{hi} \cong \overline{gj}$ and $\overline{ij} \cong \overline{gh}$. complete the proof that $\triangle ghi \cong \triangle ijg$.

	statement	reason
2	$\overline{ij} \cong \overline{gh}$	given
3	$\overline{gi} \cong \overline{gi}$	reflexive property of congruence
4	$\triangle ghi \cong \triangle ijg$

Explanation:

Step1: Identify Congruent Sides

We have three pairs of congruent sides: $\overline{HI} \cong \overline{GJ}$ (given), $\overline{IJ} \cong \overline{GH}$ (given), and $\overline{GI} \cong \overline{GI}$ (reflexive property).

Step2: Apply SSS Congruence Criterion

The Side - Side - Side (SSS) Congruence Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. For $\triangle GHI$ and $\triangle IJG$, we have:

• Side 1: $\overline{HI} \cong \overline{GJ}$
• Side 2: $\overline{IJ} \cong \overline{GH}$
• Side 3: $\overline{GI} \cong \overline{GI}$

So by the SSS Congruence Postulate, $\triangle GHI \cong \triangle IJG$.

Answer:

The reason for $\triangle GHI \cong \triangle IJG$ is the Side - Side - Side (SSS) Congruence Postulate.