Question

gle congruence
given: \\( \triangle def \cong \triangle gfe ; \angle 3 \cong \angle 7 \\)
prove: \\( \triangle dhe \cong \triangle ghf \\)
complete the statements in the two - column proof.
enter your answers in the boxes.

Explanation:

Step1: Recall vertical angles theorem

Vertical angles are the angles opposite each other when two lines cross. They are congruent. In the given figure, \(\angle DHE\) and \(\angle GHF\) are vertical angles.

Step2: Identify the angle labels

From the figure, \(\angle DHE\) is \(\angle 2\) and \(\angle GHF\) is \(\angle 5\) (or vice - versa depending on the vertex - angle correspondence).

Answer:

\(\angle 2\cong\angle 5\) (or \(\angle 5\cong\angle 2\))