Question

use the given information to prove that ∠def ≅ ∠fgd. given: (overline{de}congoverline{fg}), (overline{ef}congoverline{gd}). prove: ∠def ≅ ∠fgd

Explanation:

Step1: Identify congruent triangles

In \(\triangle DEF\) and \(\triangle FGD\), we have \(\overline{DE}\cong\overline{FG}\), \(\overline{EF}\cong\overline{GD}\), and \(\overline{DF}\) is common to both triangles. So, \(\triangle DEF\cong\triangle FGD\) (by SSS - Side - Side - Side congruence criterion).

Step2: Use corresponding parts of congruent triangles

Since \(\triangle DEF\cong\triangle FGD\), corresponding angles are congruent. So, \(\angle DEF\cong\angle FGD\) (by CPCTC - Corresponding Parts of Congruent Triangles are Congruent).

Answer:

We have proven that \(\angle DEF\cong\angle FGD\) using SSS congruence criterion for \(\triangle DEF\) and \(\triangle FGD\) and then CPCTC.