Question

which of the following is a true statement?

options:

• ( mangle bac = mangle cad )
• ( mangle bac < mangle cad )
• ( mangle bac > mangle cad )
• ( mangle bac leq mangle cad )

Explanation:

Step1: Recall triangle angle-side relation

In any triangle, the larger side is opposite the larger angle.

Step2: Analyze $\triangle ABC$

In $\triangle ABC$, $AB=8$, $BC=12$, $AC$ is common. The side opposite $\angle BAC$ is $BC=12$.

Step3: Analyze $\triangle ADC$

In $\triangle ADC$, $AD=8$, $DC=8$, $AC$ is common. The side opposite $\angle CAD$ is $DC=8$.

Step4: Compare the angles

Since $12>8$, the angle opposite the longer side ($\angle BAC$) is larger than the angle opposite the shorter side ($\angle CAD$).

Answer:

$\boldsymbol{m\angle BAC > m\angle CAD}$