Question

given ab//cd. prove that △abc≌△cda.

Explanation:

Step1: Use the property of parallel lines

Since \(AB\parallel CD\), by the alternate - interior angles theorem, \(\angle BAC\cong\angle DCA\) (because \(AC\) is a transversal).

Step2: Identify right angles

We know that \(\angle ABC\) and \(\angle CDA\) are right angles. So \(\angle ABC\cong\angle CDA = 90^{\circ}\).

Step3: Use the AAS (Angle - Angle - Side) congruence criterion

We have two pairs of congruent angles (\(\angle BAC\cong\angle DCA\) and \(\angle ABC\cong\angle CDA\)) and a pair of congruent non - included sides (\(AC = CA\) as a common side).

Answer:

\(\triangle ABC\cong\triangle CDA\) by AAS. The first unknown angle is \(\angle BAC\) (corresponding to \(\angle DCA\)) and the second unknown triangle is \(\triangle CDA\).