Question

Cd bisects ∠acb. Which of the following statements must be true?

1) bdac = cdm
2) ∠acd = m∠bcd
3) m∠cda = m∠cdb
4) m∠dca = m∠dac

Answer 1

If CD bisects ∠ACB in a triangle, m∠CDA equals m∠CDB because the bisecting line divides the angle into two equal parts.

Step-by-step explanation:

The question is asking about the properties of angles when a line segment bisects an angle in a triangle. If CD bisects ∠ACB, then statement 3, which states that m∠CDA = m∠CDB, must be true. Because CD bisects ∠ACB, it divides it into two equal angles. Therefore, the measure of angle CDA is equal to the measure of angle CDB, and we can represent them with the same variable (e.g., m∠CDA = m∠CDB = x degrees).