Question

parallelogram abcd is shown with diagonal bd. move options to the spaces to complete the proof that △abd≅△cdb. statement reason abcd is a parallelogram. given ∠cbd≅∠adb ________________ are congruent. __≅__ opposite sides of a parallelogram are congruent. __≅__ reflexive property △abd≅△cdb ________________ congruency alternate interior angles corresponding angles (overline{ab}) (overline{bc}) (overline{bd}) (overline{cd}) (overline{da}) side side angle side angle side

Explanation:

Step1: Identify angle - congruence reason

Since $AB\parallel CD$ in parallelogram $ABCD$, $\angle CBD$ and $\angle ADB$ are alternate - interior angles. So the reason for $\angle CBD\cong\angle ADB$ is "Alternate Interior angles".

Step2: Identify congruent sides

In parallelogram $ABCD$, opposite sides are congruent. So $AB\cong CD$ and $AD\cong BC$. We can choose $AB\cong CD$ for the proof.

Step3: Identify the reflexive - property side

The common side for $\triangle ABD$ and $\triangle CDB$ is $BD$. So $BD\cong BD$ by the reflexive property.

Step4: Identify the congruence postulate

We have a pair of congruent angles ($\angle CBD\cong\angle ADB$), a pair of congruent sides ($AB\cong CD$) and the included side ($BD\cong BD$). So $\triangle ABD\cong\triangle CDB$ by the Side - Angle - Side (SAS) congruence postulate.

Answer:

Statement	Reason
$\angle CBD\cong\angle ADB$	Alternate Interior angles are congruent.
$\overline{AB}\cong\overline{CD}$	Opposite sides of a parallelogram are congruent.
$\overline{BD}\cong\overline{BD}$	Reflexive property
$\triangle ABD\cong\triangle CDB$	Side Angle Side Congruency