Question

decide whether the statement about the diagram is true and explain your answer using the definitions that you have learned. see example 4 m∠abc = 90° pq⊥rs

Explanation:

Step1: Recall right - angle definition

A right - angle is an angle that measures 90 degrees. In the first diagram, there is a right - angle symbol at $\angle ABC$.

Step2: Determine truth of statement

Since the right - angle symbol indicates that $\angle ABC = 90^{\circ}$, the statement $m\angle ABC=90^{\circ}$ is true.

Step3: Recall perpendicular lines definition

Perpendicular lines intersect at a right - angle (90 degrees). In the second diagram, there is a right - angle symbol at the intersection of lines $\overleftrightarrow{PQ}$ and $\overleftrightarrow{RS}$.

Step4: Determine truth of statement

Since the right - angle symbol indicates that the lines intersect at 90 degrees, the statement $\overleftrightarrow{PQ}\perp\overleftrightarrow{RS}$ is true.

Answer:

The statement $m\angle ABC = 90^{\circ}$ is true. The statement $\overleftrightarrow{PQ}\perp\overleftrightarrow{RS}$ is true.