Question

cd bisects ∠acb. which statements must be true? check all that apply. ad = bd ac = cd m∠acd = m∠bcd m∠cda = m∠cdb m∠dca = m∠dac

Explanation:

Step1: Recall angle bisector definition

An angle bisector splits an angle into two equal parts. Since $\overline{CD}$ bisects $\angle ACB$, $\angle ACD$ and $\angle BCD$ are equal.

Step2: Analyze other statements

• $AD=BD$: Only true if $\triangle ACB$ is isosceles with $AC=BC$, not given.
• $AC=CD$: No info supports this equality.
• $m\angle CDA=m\angle CDB$: Only true if $CD\perp AB$, not given.
• $m\angle DCA=m\angle DAC$: Only true if $AD=CD$, not given.

Answer:

m∠ACD = m∠BCD