Question

given: $overline{ac}$ bisects $angle bad$ and $angle bcd$. prove: $\triangle abccong\triangle adc$ 2. $angle baccongangle dac$ and $angle bcacongangle acd$ 2. definition of an angle - bisector 3. $overline{ac}congoverline{ac}$ 3. reflexive property 4. click here to insert 4. click here to insert

Explanation:

Step1: Recall given and previous steps

We know $\angle BAC\cong\angle DAC$, $\angle BCA\cong\angle ACD$ and $AC\cong AC$.

Step2: Apply congruence postulate

By ASA (two angles and the included side of one triangle are congruent to two angles and the included side of another triangle), $\triangle ABC\cong\triangle ADC$.

Answer:

1. $\triangle ABC\cong\triangle ADC$; 4. Angle - Side - Angle (ASA) Congruence Postulate