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.

Answer 1

True:
- AD bisects ∠BAC.

False:
- AD bisects BC.
- AD forms right angles with BC.
- AD is perpendicular to BC.
- AD is the perpendicular bisector of BC.

Reason: Making ∠BAD = ∠CAD makes AD the angle bisector of ∠BAC. That does not in general make D the midpoint of BC or make AD perpendicular to BC—those only hold in special cases (e.g. an isosceles triangle with AB = AC, or other special configurations).