Question

1. based on the construction below, which statement must be true? in proving this construction, which reason is used for the congruence involved? (1) m∠abd = 1/2 m∠cbd (2) m∠abd = m∠cbd (3) m∠abd = m∠abc (4) m∠cbd = 1/2m∠abd

Explanation:

Step1: Identify angle - bisector construction

The construction shown is of an angle - bisector. An angle - bisector divides an angle into two equal angles.

Step2: Determine the equal angles

Ray $BD$ is the angle - bisector of $\angle ABC$. So, $\angle ABD$ and $\angle CBD$ are equal in measure, i.e., $m\angle ABD=m\angle CBD$.

Answer:

(2) $m\angle ABD = m\angle CBD$