Question

prove: $adcong cd$. step statement reason 1 $bd$ bisects $angle abc$ $bd$ bisects $angle adc$ 2 $angle abdcongangle cbd$ 3 $angle adbcongangle cdb$ 4 $bdcong bd$ 5 $\triangle abdcong\triangle cbd$ 6 $adcong cd$ answer attempt 1 out of 2 step 1 reason = step 2 reason = step 3 reason = step 4 reason = step 5 reason = step 6 reason =

Explanation:

Step1: Given information

Given that $BD$ bisects $\angle ABC$ and $BD$ bisects $\angle ADC$.

Step2: Definition of angle - bisector

By the definition of an angle - bisector, if $BD$ bisects $\angle ABC$, then $\angle ABD\cong\angle CBD$.

Step3: Definition of angle - bisector

Since $BD$ bisects $\angle ADC$, by the definition of an angle - bisector, $\angle ADB\cong\angle CDB$.

Step4: Reflexive property

$BD$ is common to both $\triangle ABD$ and $\triangle CBD$, so $BD\cong BD$ by the reflexive property of congruence.

Step5: Angle - Side - Angle (ASA) congruence criterion

In $\triangle ABD$ and $\triangle CBD$, we have $\angle ABD\cong\angle CBD$, $BD\cong BD$, and $\angle ADB\cong\angle CDB$. So, $\triangle ABD\cong\triangle CBD$ by the ASA congruence criterion.

Step6: Corresponding parts of congruent triangles

Since $\triangle ABD\cong\triangle CBD$, then $AD\cong CD$ because corresponding parts of congruent triangles are congruent (CPCTC).

Answer:

Step 1 Reason: Given
Step 2 Reason: Definition of angle - bisector
Step 3 Reason: Definition of angle - bisector
Step 4 Reason: Reflexive property
Step 5 Reason: ASA congruence criterion
Step 6 Reason: CPCTC