Question

question fill in the missing statement and reason of the proof below. given: \\( \overline { g h } \cong \overline { e h } \\), \\( \overline { d h } \cong \overline { f h } \\) and \\( \angle c d h \cong \angle c f h \\). prove: \\( \angle a \cong \angle b \\).

Explanation:

Step1: <Identify congruent triangles>

Since \( \overline{GH}\cong\overline{EH}\), \( \overline{DH}\cong\overline{FH}\), and \( \angle CDH\cong\angle CFH\), by the Side - Angle - Side (SAS) congruence criterion, \(\triangle GHD\cong\triangle EHF\).

Step2: <Use congruent triangles property>

If \(\triangle GHD\cong\triangle EHF\), then their corresponding angles \( \angle A\) (which is an angle in \(\triangle GHD\)) and \( \angle B\) (which is an angle in \(\triangle EHF\)) are congruent.

Answer:

\(\triangle GHD\cong\triangle EHF\) (by SAS congruence criterion)