Question

∠adb and ∠cdb are right angles
reason: perpendicular lines form right angles
△abd and △cbd are right triangles
reason: the triangles each contain a right angle
ab≅cb
reason: select reason
ed≅bd
reason: select reason
△abd≅△cbd
reason: select reason

Explanation:

Step1: Identify given equal - side information

We are given that $\overline{AB}\cong\overline{CB}$ and $\overline{BD}\cong\overline{BD}$ (the common side for both $\triangle ABD$ and $\triangle CBD$).

Step2: Recall congruence criteria for right - triangles

For right - triangles, the Hypotenuse - Leg (HL) congruence criterion states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent. In $\triangle ABD$ and $\triangle CBD$, $\overline{AB}$ and $\overline{CB}$ can be considered as hypotenuses (if we assume the right - angles at $\angle ADB$ and $\angle CDB$) and $\overline{BD}$ is a common leg.

Answer:

For $\overline{AB}\cong\overline{CB}$, the reason could be "Given". For $\overline{BD}\cong\overline{BD}$, the reason is "Reflexive Property of Congruence". For $\triangle ABD\cong\triangle CBD$, the reason is "Hypotenuse - Leg (HL) Congruence Theorem"