Question

13 triangle abc with right angle bdc is shown below. which additional fact is needed to prove △abd ≅ △cbd by side - angle - side (sas)? options: ( ad = cd ), ( angle bad cong angle bcd ), ( angle abd cong angle cbd ), ( ab = cb ) (diagram: triangle ( abc ) with ( d ) on ( ac ), ( angle bdc ) is a right angle, ( bd ) connects ( b ) to ( d ))

Explanation:

Answer:

To prove \( \triangle ABD \cong \triangle CBD \) by SAS, we need two sides and the included angle. We know \( BD \) is common (side), and \( \angle ADB = \angle CDB = 90^\circ \) (angle). So we need \( AD = CD \) (side) to satisfy SAS. Among the options, \( \boldsymbol{AD = CD} \) (first option) is the additional fact needed.