given: ∠ghd and ∠edh are right; (overline{gh}congoverline{ed}). which relationship in the diagram is true…
given: ∠ghd and ∠edh are right; (overline{gh}congoverline{ed}). which relationship in the diagram is true? △ghd≅△edh by sas △ghf≅△edf by sss △fdh≅△fde by asa △hfd≅△hfg by sss
Answer
Explanation:
Step1: Analyze given information
We have $\angle GHD=\angle EDH = 90^{\circ}$ and $\overline{GH}\cong\overline{ED}$. Also, $\overline{HD}$ is common to $\triangle GHD$ and $\triangle EDH$.
Step2: Recall congruence postulates
The Side - Angle - Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In $\triangle GHD$ and $\triangle EDH$, $\overline{GH}\cong\overline{ED}$, $\angle GHD\cong\angle EDH$ and $\overline{HD}\cong\overline{HD}$.
Answer:
$\triangle GHD\cong\triangle EDH$ by SAS