5. given:
$\overline{ab} \cong \overline{cb}$
$\overline{bd}$ bisects $\angle abc$
prove:
$\angle a \cong \angle c$
statement reason

Question

Accepted Answer

# Explanation:
## Step1: State given congruent sides
$\overline{AB} \cong \overline{CB}$ (Given)
## Step2: State angle bisector definition
$\overline{BD}$ bisects $\angle ABC$, so $\angle ABD \cong \angle CBD$ (Definition of angle bisector)
## Step3: State common side
$\overline{BD} \cong \overline{BD}$ (Reflexive Property of Congruence)
## Step4: Apply SAS congruence
$	riangle ABD \cong 	riangle CBD$ (Side-Angle-Side (SAS) Congruence Postulate)
## Step5: Corresponding parts of congruent triangles are congruent
$\angle A \cong \angle C$ (CPCTC: Corresponding Parts of Congruent Triangles are Congruent)

# Answer:
| STATEMENT | REASON |
|-----------|--------|
| $\overline{AB} \cong \overline{CB}$ | Given |
| $\angle ABD \cong \angle CBD$ | Definition of angle bisector |
| $\overline{BD} \cong \overline{BD}$ | Reflexive Property of Congruence |
| $	riangle ABD \cong 	riangle CBD$ | SAS Congruence Postulate |
| $\angle A \cong \angle C$ | CPCTC |

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QUESTION IMAGE

Question

Explanation:

Step1: State given congruent sides

Step2: State angle bisector definition

Step3: State common side

Step4: Apply SAS congruence

Step5: Corresponding parts of congruent triangles are congruent

Answer:

STATEMENT	REASON
$\angle ABD \cong \angle CBD$	Definition of angle bisector
$\overline{BD} \cong \overline{BD}$	Reflexive Property of Congruence
$\triangle ABD \cong \triangle CBD$	SAS Congruence Postulate
$\angle A \cong \angle C$	CPCTC