Question

1. given: $overline{gi}congoverline{jl}$, $overline{gh}congoverline{kl}$ prove: $overline{hi}congoverline{jk}$ statements reasons $gicong jl,ghcong kl$ guin

Explanation:

Step1: Recall segment - addition postulate

$GI = GH+HI$ and $JL=JK + KL$

Step2: Use the given congruences

Since $\overline{GI}\cong\overline{JL}$, then $GI = JL$; since $\overline{GH}\cong\overline{KL}$, then $GH = KL$

Step3: Substitute the segment - addition expressions

$GH + HI=JK + KL$

Step4: Substitute $GH$ with $KL$

$KL+HI=JK + KL$

Step5: Subtract $KL$ from both sides

$HI=JK$

Step6: Write the congruence statement

$\overline{HI}\cong\overline{JK}$

Answer:

$\overline{HI}\cong\overline{JK}$