Question

line bc, line de, and ray af intersect at point a. select all statements that are true about the diagram below.
□∠dac≅∠bae
□∠dac≅∠cae
□∠dab≅∠cae
□∠baf≅∠fae
□∠dac + ∠cae = 180
□∠baf + ∠bad = 180

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. $\angle DAC$ and $\angle BAE$ are vertical angles, so $\angle DAC\cong\angle BAE$.

Step2: Analyze linear - pair property

A linear pair of angles is supplementary. $\angle BAF$ and $\angle BAD$ form a linear pair, so $\angle BAF+\angle BAD = 180^{\circ}$.

Step3: Check other angle - relationships

$\angle DAC$ and $\angle CAE$ are not congruent in general, $\angle DAB$ and $\angle CAE$ are not congruent, $\angle BAF$ and $\angle FAE$ are not congruent in general, and $\angle DAC+\angle CAE$ is not necessarily $180^{\circ}$.

Answer:

$\angle DAC\cong\angle BAE$, $\angle BAF+\angle BAD = 180$