Question

given $overline{bd}$ bisects $angle abc$, complete the flowchart proof below. $overline{bd}$ bisects $angle abc$. reason: given. $angle abdcongangle cbd$. reason:. $angle acongangle c$. reason:. $overline{ab}congoverline{cb}$. reason:. $\triangle abdcong\triangle cbd$. reason:.

Explanation:

Step1: Definition of angle - bisector

By the definition of an angle - bisector, if a ray bisects an angle, it divides the angle into two congruent angles. Since $\overline{BD}$ bisects $\angle ABC$, we have $\angle ABD\cong\angle CBD$.

Step2: Given (assumed from figure or context)

The reason for $\angle A\cong\angle C$ is likely given in the problem's context (perhaps it was an additional given statement not fully shown).

Step3: Given (assumed from figure or context)

The reason for $\overline{AB}\cong\overline{CB}$ is likely given in the problem's context (perhaps it was an additional given statement not fully shown).

Step4: ASA (Angle - Side - Angle) congruence criterion

In $\triangle ABD$ and $\triangle CBD$, we have $\angle ABD\cong\angle CBD$ (from Step 1), $\overline{AB}\cong\overline{CB}$ (from Step 3), and $\angle A\cong\angle C$ (from Step 2). By the ASA congruence criterion, $\triangle ABD\cong\triangle CBD$.

Answer:

• $\angle ABD\cong\angle CBD$ Reason: Definition of angle - bisector
• $\angle A\cong\angle C$ Reason: Given
• $\overline{AB}\cong\overline{CB}$ Reason: Given
• $\triangle ABD\cong\triangle CBD$ Reason: ASA congruence criterion