Question

given: ( abparallel cd ) and ( adparallel bc ) prove: ( \triangle acdcong\triangle cab ) complete the proof by selecting the correct reason that completes the proof. for reason (4): asa postulate aas postulate sas postulate

Explanation:

Step1: Recall the ASA (Angle - Side - Angle) Postulate

The ASA Postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Analyze the given information

We have \(\angle BAC=\angle DCA\) (from \(AB\parallel CD\), alternate - interior angles), \(\angle BCA = \angle DAC\) (from \(AD\parallel BC\), alternate - interior angles), and \(AC = AC\) (common side).

Step3: Apply the ASA Postulate

Since we have two pairs of congruent angles (\(\angle BAC=\angle DCA\) and \(\angle BCA=\angle DAC\)) and the included side (\(AC\)) is common (so congruent to itself), by the ASA Postulate, \(\triangle ABC\cong\triangle CDA\). Then, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \(\angle ACD=\angle CAB\).

Answer:

ASA Postulate