Question

adjust point d so the measure of angle bad is equal to the measure of angle cad. which statements are true? check all that apply. ad bisects ∠bac. ad bisects bc. ad forms right angles with bc. ad is perpendicular to bc. ad is the perpendicular bisector of bc. m∠ bad = 20° bd = 18 units m∠ cad = 54° dc = 42 units

Explanation:

Step1: Check angle bisector definition

An angle bisector splits an angle into two equal parts. The problem requires $m\angle BAD = m\angle CAD$, so $\overline{AD}$ bisects $\angle BAC$.

Step2: Check BC bisector condition

A segment bisector splits $\overline{BC}$ into equal parts. Given $BD=18$ and $DC=42$ (unequal), $\overline{AD}$ does not bisect $\overline{BC}$.

Step3: Check right angle/perpendicular

Right angles mean $90^\circ$, but no info shows $\overline{AD} \perp \overline{BC}$. Perpendicular bisector needs both bisecting and right angles, which fails.

Answer:

$\overline{AD}$ bisects $\angle BAC$.