Question

CD bisects ∠ACB. Which statements must be true? Check all that apply.

1. AD = BD
2. AC = CD
3. m∠ACD = m∠BCD
4. m∠CDA = m∠CDB
5. m∠DCA = m∠DAC

Answer 1

Answer: A, C, D

Explanation:

1) AD=BD must be true because the angle bisector drawn from the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

2) AC=CD does not need to be true because angles ADC and CAD do not need to be congruent.

3) This must be true by the definition of an angle bisector.

4) This must be true because angles CDA and CDB are both right angles.

5) This does not need to be true because triangle ADC does not need to be isosceles.