Question

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

If $\overleftrightarrow{\mathit{\text{NM}}}\mathit{\perp }\overleftrightarrow{\mathit{\text{GH}}}$, then$\angle \mathbf{3}$and$\angle 4$complementary.

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 as $\overleftrightarrow{NM}\perp \overleftrightarrow{GH}$, then $\angle MNH={90}^{\circ }$and $\angle MNK=\angle MNH$as perpendicular lines make an angle of ${90}^{\circ }$.

So, $\angle 3$and $\angle 4$are complimentary.

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