Question

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

If $\overline{AB}\perp \overline{CE}$, then $\angle ADC\cong \angle ADE$.

Short answer

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

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the theorem of perpendicular lines.

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

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

Given that $\overline{AB}\perp \overline{CE}$.

That implies the lines AB and CE are perpendicular lines.

Therefore, by using the theorem of perpendicular lines it can be said that the lines AB and CE will form the adjacent congruent angles.

That implies, $\angle ADC\cong \angle ADE$.

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