Question

question
in the diagram below, \\( \angle d \cong \angle g, \angle e \cong \angle h \\). enter segments in the blanks provided
that would result in a true equation.
answer attempt 1 out of 2

Explanation:

Step1: Use the Angle - Angle (AA) similarity criterion

If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Here, \(\angle D\cong\angle G\) and \(\angle E\cong\angle H\), so \(\triangle CDE\sim\triangle FGH\) by AA similarity.

Step2: Use the property of similar triangles

In similar triangles, corresponding sides are proportional. The correspondence of angles gives the correspondence of sides. Since \(\angle D\) corresponds to \(\angle G\) and \(\angle E\) corresponds to \(\angle H\), then \(\overline{CD}\) corresponds to \(\overline{FG}\), \(\overline{DE}\) corresponds to \(\overline{GH}\), and \(\overline{CE}\) corresponds to \(\overline{FH}\)

Answer:

\(\overline{CD}\cong\overline{FG}\) (or other correct corresponding side pairs like \(\overline{DE}\cong\overline{GH}\), \(\overline{CE}\cong\overline{FH}\))