Question

Given: $\angle ABD\cong \angle AED$

Prove: $\angle C\cong \angle F$

Short answer

It is proved that $\mathbf{\angle }\mathit{C}\mathbf{\cong }\mathbf{\angle }\mathit{F}$.

Step-by-step solution

Step 1. Observe the figure and highlight angle C and angle F .

Step 2. Apply the definition of vertically opposite angles.

Vertically opposite angles are the opposite angles formed due to intersection of two lines.

Consider $\Delta BDC\text{and}\Delta EDF$,

$\angle BDC\text{and}\angle EDF$are vertically opposite angles, therefore, $\angle BDC=\angle EDF$.

Also, $\angle DBC=\angle DEF$.

Step 3. Apply corollary 1.

If two angles of one triangle are congruent to two angles of another triangle then third angles are congruent.

Therefore, $\angle C\cong \angle F$.