Q16 - Geometry

Question

Complete.

If $\overline{DB}$ bisects $\angle CDA$ then $\angle ?\cong \angle ?$.

Step-by-Step Solution

Answer

If $\overline{DB}$ bisects $\angle CDA$ then $\mathit{m}\mathbf{\angle }\mathbf{6}\mathbf{\cong }\mathit{m}\mathbf{\angle }\mathbf{5}$.

Step 1. Write definition of angle bisector.

An angle bisector is a line segment which divides an angle into two congruent angles, that is, angles with same measure.

Step 2. Description of step.

From the given figure, it can be observe that the $\overline{DB}$ divides $\angle CDA$ into two angles, $\angle CDA$ and $\angle ADB$, with same measure.

Step 3. Write the two congruent angles formed due to bisector, D B

$\begin{array}{l}m\angle CDB\cong m\angle ADB\\ m\angle 6\cong m\angle 5\end{array}$