MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

Answer with explanation:it is given that ,in ΔABC, ∠BAD=20°, and ∠CAD=54°We have to adjust point D,so that measure of angle BAD is equal to the measure of angle CAD.that is, if point D is moved to right of B,then ∠BAD increases from 20° to (20+x)° and ∠CAD decreases from 54° to (54-x)°.→20 +x=54-x⇒ 2 x= 54 -20⇒2 x=34x=17°Using angle bisector theorem, if AD bisects ∠B AC.[tex]\frac{BA}{AC}=\frac{BD}{DC}[/tex]so,If, ∠BAD=∠CAD=37°, then1. AD bisects ∠B AC.→→→Option A