Question

State which definition, postulate, or theorem justifies the statement about the diagram.

If $\angle 1\cong \angle 2$, then $\overrightarrow{AD}$ is the bisector of $\angle BAC$.

Short answer

The angle bisector theorem justifies the statement about the diagram.

Step-by-step solution

Step 1. Observe the given diagram.

The diagram constitutes a triangle ABC and $\angle 1\cong \angle 2$.

Step 2. State the angle bisector theorem.

The theorem states that if a line bisects an angle of a triangle, then that line divides the opposite side of that angle into two segments proportional to other two sides of the triangle.

Step 3. State the conclusion.

Considering the given diagram and the statement: “if $\angle 1\cong \angle 2$then $\overrightarrow{AD}$is the bisector of $\angle BAC$”.

Therefore, the statement about the diagram is justified by the angle bisector theorem.