Question

Name the definition or state the theorem that justifies the statement about the diagram.

If $\overleftrightarrow{\mathit{\text{NM}}}\mathit{\perp }\overleftrightarrow{\mathit{\text{GH}}}$, thenrole="math" localid="1646274625116" $\mathit{\angle }\mathit{\text{MNK}}\mathit{\cong }\mathit{\angle }\mathit{\text{MNH}}$

Short answer

The statement regarding the diagram can justified by the Definition of perpendicular lines.

Step-by-step solution

Step 1. Observe the diagram.

Here,$\overleftrightarrow{NM}\perp \overleftrightarrow{GH}$.

Step 2. State the definition of perpendicular lines.

The angle formed by two perpendicular lines is congruent adjacent angle.

Step 3. State the conclusion.

Considering the diagram and $\overleftrightarrow{NM}\perp \overleftrightarrow{GH}$, then $\angle 3$and $\angle 4$are complimentary.

Thus, $\angle MNK\cong \angle MHK$.

Therefore, the statement is justified by the definition of perpendicular lines.