Question

based on the given diagram, complete the flowchart proof below. ∠adb≅∠cdb reason: select reason ∠a≅∠c reason: select reason bd≅bd reason: select reason △abd≅△cbd reason: select reason

Explanation:

Step1: Identify angle - type

$\angle ADB$ and $\angle CDB$ are right - angles (from the diagram's markings), so $\angle ADB\cong\angle CDB$ by the definition of right - angles (all right - angles are congruent).

Step2: Given information

$\angle A\cong\angle C$ is given.

Step3: Reflexive property

$\overline{BD}\cong\overline{BD}$ by the reflexive property of congruence (a segment is congruent to itself).

Step4: Determine triangle congruence

Since we have two pairs of congruent angles ($\angle A\cong\angle C$, $\angle ADB\cong\angle CDB$) and a pair of congruent sides ($\overline{BD}\cong\overline{BD}$), $\triangle ABD\cong\triangle CBD$ by the Angle - Angle - Side (AAS) congruence criterion.

Answer:

• $\angle ADB\cong\angle CDB$ Reason: Definition of right - angles (all right - angles are congruent)
• $\angle A\cong\angle C$ Reason: Given
• $\overline{BD}\cong\overline{BD}$ Reason: Reflexive property of congruence
• $\triangle ABD\cong\triangle CBD$ Reason: Angle - Angle - Side (AAS) congruence criterion