Question

Write the name or statement of the definition, postulate, or theorem that justifies the statement about the diagram.

If $\angle FDG\cong \angle GDH$, then $\overleftrightarrow{DG}\perp \overleftrightarrow{HF}$.

Short answer

The name of the theorem which justifies the statement about the given diagram is theorem of converse of perpendicular lines.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the theorem of converse of perpendicular lines.

The theorem of converse of perpendicular lines states that if the two lines form the adjacent congruent angles, then the lines are perpendicular.

Step 3. Write the name of the theorem that justifies the statement about the given diagram.

Given that $\angle FDG\cong \angle GDH$.

That implies the angles FDG and GDH are congruent angles.

From the given diagram it can be noticed that the angles FDG and GDH are adjacent angles.

That implies the angles FDG and GDH are adjacent congruent angles.

Therefore, by using the theorem of the converse of perpendicular lines it can be said that the lines DG and HF are perpendicular.

That implies, $\overleftrightarrow{DG}\perp \overleftrightarrow{HF}$.

Therefore, the name of the theorem that justifies the statement about the given diagram is theorem of converse of perpendicular lines.