Question

isosceles triangle abc is shown, with angle bisector ad. move options to the blanks to complete the proof that the base angles of an isosceles triangle are congruent.

statement	reason
	definition of angle bisector
ad ≅ ad
△bad ≅ △cad	side - angle - side
	corresponding parts of congruent triangles are congruent
ba ≅ ca	definition of isosceles
db ≅ dc
∠adb ≅ ∠adc	reflexive property
∠bad ≅ ∠cad

|∠b ≅ ∠c|right angles are congruent.

Explanation:

Step1: State the given information

$\triangle ABC$ is isosceles, $AD$ is an angle - bisector (Given)

Step2: Use the definition of angle - bisector

$\angle BAD\cong\angle CAD$ (Definition of angle bisector)

Step3: Apply the reflexive property

$\overline{AD}\cong\overline{AD}$ (Reflexive property)

Step4: Prove triangle congruence

$\triangle BAD\cong\triangle CAD$ (Side - Angle - Side)

Step5: Use the property of congruent triangles

$\angle B\cong\angle C$ (Corresponding parts of congruent triangles are congruent)

Answer:

1. $\angle BAD\cong\angle CAD$; Definition of angle bisector
2. $\overline{AD}\cong\overline{AD}$; Reflexive property
3. $\triangle BAD\cong\triangle CAD$; Side - Angle - Side
4. $\angle B\cong\angle C$; Corresponding parts of congruent triangles are congruent