triangle abc is shown, with angle bisector $\overline{ad}$.
move options to the blanks to complete the proof that the base angles of an isosceles triangle are congruent.
| statement | reason |
| --- | --- |
| $\triangle abc$ is isosceles; $\overline{ad}$ is an angle bisector | given |
| | |
| | definition of angle bisector |
| $\overline{ad} \cong \overline{ad}$ | |
| $\triangle bad \cong \triangle cad$ | side - angle - side |
| | corresponding parts of congruent triangles are congruent. |
options: $\overline{ba} \cong \overline{ca}$, $\overline{db} \cong \overline{dc}$, $\angle adb \cong \angle adc$, $\angle bad \cong \angle cad$, $\angle b \cong \angle c$, definition of isosceles, reflexive property, right angles are congruent.

Question

triangle abc is shown, with angle bisector $\overline{ad}$.
move options to the blanks to complete the proof that the base angles of an isosceles triangle are congruent.
| statement | reason |
| --- | --- |
| $\triangle abc$ is isosceles; $\overline{ad}$ is an angle bisector | given |
|  |  |
|  | definition of angle bisector |
| $\overline{ad} \cong \overline{ad}$ |  |
| $\triangle bad \cong \triangle cad$ | side - angle - side |
|  | corresponding parts of congruent triangles are congruent. |
options: $\overline{ba} \cong \overline{ca}$, $\overline{db} \cong \overline{dc}$, $\angle adb \cong \angle adc$, $\angle bad \cong \angle cad$, $\angle b \cong \angle c$, definition of isosceles, reflexive property, right angles are congruent.

Accepted Answer

# Explanation:
## Step1: Fill isosceles side statement
$\overline{BA} \cong \overline{CA}$
## Step2: Fill isosceles side reason
Definition of isosceles
## Step3: Fill angle bisector statement
$\angle BAD \cong \angle CAD$
## Step4: Fill reflexive property reason
Reflexive property
## Step5: Fill congruent angles statement
$\angle B \cong \angle C$

# Answer:
| Statement | Reason |
|-----------|--------|
| $	riangle ABC$ is isosceles; $\overline{AD}$ is an angle bisector | Given |
| $\overline{BA} \cong \overline{CA}$ | Definition of isosceles |
| $\angle BAD \cong \angle CAD$ | Definition of angle bisector |
| $\overline{AD} \cong \overline{AD}$ | Reflexive property |
| $	riangle BAD \cong 	riangle CAD$ | Side-Angle-Side |
| $\angle B \cong \angle C$ | Corresponding parts of congruent triangles are congruent. |

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QUESTION IMAGE

Question

Explanation:

Step1: Fill isosceles side statement

Step2: Fill isosceles side reason

Step3: Fill angle bisector statement

Step4: Fill reflexive property reason

Step5: Fill congruent angles statement

Answer:

statement	reason

	definition of angle bisector
\\(\overline{ad} \cong \overline{ad}\\)
\\(\triangle bad \cong \triangle cad\\)	side - angle - side
	corresponding parts of congruent triangles are congruent.

Statement	Reason
$\overline{BA} \cong \overline{CA}$	Definition of isosceles
$\angle BAD \cong \angle CAD$	Definition of angle bisector
$\overline{AD} \cong \overline{AD}$	Reflexive property
$\triangle BAD \cong \triangle CAD$	Side-Angle-Side
$\angle B \cong \angle C$	Corresponding parts of congruent triangles are congruent.