Question

∠adb and ∠cdb are right angles. reason: perpendicular lines form right angles. ∠adb≅∠cdb. reason: select reason. ad≅cd. reason: select reason. ∠a≅∠c. reason: select reason. △abd≅△cbd. reason: select reason.

Explanation:

Step1: Reason for ∠ADB≅∠CDB

All right - angles are congruent. Since ∠ADB and ∠CDB are right - angles, ∠ADB≅∠CDB.

Step2: Reason for AD≅CD

Given (assuming this is a given condition in the overall problem context).

Step3: Reason for ∠A≅∠C

Given (assuming this is a given condition in the overall problem context).

Step4: Reason for △ABD≅△CBD

By the Angle - Side - Angle (ASA) congruence criterion. We have ∠ADB≅∠CDB (right - angles), AD≅CD, and ∠A≅∠C.

Answer:

∠ADB≅∠CDB Reason: All right - angles are congruent; AD≅CD Reason: Given; ∠A≅∠C Reason: Given; △ABD≅△CBD Reason: ASA congruence criterion.