Question

1. given: $overrightarrow{bd}$ bisects $angle abc$ prove: $angle 2congangle 3$ statements reasons 1. $overrightarrow{bd}$ bisects $angle abc$ 1. given 2. $angle 1congangle 2$ 2. 3. 3. definition of vertical angles 4. 4. 5. 5.

Explanation:

Step1: Recall angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, by the definition of an angle - bisector, $\angle 1\cong\angle 2$.

Step2: Identify vertical angles

$\angle 1$ and $\angle 3$ are vertical angles. By the definition of vertical angles, $\angle 1\cong\angle 3$.

Step3: Use the transitive property of congruence

Since $\angle 1\cong\angle 2$ and $\angle 1\cong\angle 3$, by the transitive property of congruence (if $a = b$ and $a = c$, then $b = c$ for congruent angles), $\angle 2\cong\angle 3$.

Filling in the table:

Statements	Reasons
2. $\angle 1\cong\angle 2$	2. Definition of angle - bisector
3. $\angle 1\cong\angle 3$	3. Definition of vertical angles
4. $\angle 2\cong\angle 3$	4. Transitive property of congruence
5.	5.

Answer:

The completed table shows the proof that $\angle 2\cong\angle 3$ with the reasons provided for each statement.