Question

ac bisects ∠bad
given
∠bac ≅ ∠dac
reason:
select reason
∠b ≅ ∠d
reason:
select reason
ac ≅ ac
reason:
select reason
△abc ≅ △adc
reason:
select reason

Explanation:

Step1: Determine the reason for \(\angle BAC\cong\angle DAC\)

Since \(AC\) bisects \(\angle BAD\), by the definition of an angle - bisector, it divides \(\angle BAD\) into two congruent angles. So the reason for \(\angle BAC\cong\angle DAC\) is "Definition of angle bisector".

Step2: Determine the reason for \(\angle B\cong\angle D\)

Assume this is given information (as there is no prior derivation shown in the provided flow - chart for this congruence). So the reason for \(\angle B\cong\angle D\) is "Given".

Step3: Determine the reason for \(AC\cong AC\)

By the reflexive property of congruence, any segment is congruent to itself. So the reason for \(AC\cong AC\) is "Reflexive property of congruence".

Step4: Determine the reason for \(\triangle ABC\cong\triangle ADC\)

We have \(\angle BAC\cong\angle DAC\) (from Step 1), \(\angle B\cong\angle D\) (from Step 2), and \(AC\cong AC\) (from Step 3). By the AAS (Angle - Angle - Side) congruence criterion, \(\triangle ABC\cong\triangle ADC\). So the reason for \(\triangle ABC\cong\triangle ADC\) is "AAS (Angle - Angle - Side)".

Answer:

• For \(\angle BAC\cong\angle DAC\): Definition of angle bisector
• For \(\angle B\cong\angle D\): Given
• For \(AC\cong AC\): Reflexive property of congruence
• For \(\triangle ABC\cong\triangle ADC\): AAS (Angle - Angle - Side)