Question

given: abcd is a parallelogram. prove: ab ≅ cd and bc ≅ da. assemble the proof by dragging tiles to the statements and reasons columns.

Explanation:

Step1: Draw diagonal AC

In parallelogram ABCD, draw diagonal AC.

Step2: Use property of parallel lines

Since AB∥CD and AD∥BC, ∠BAC = ∠DCA (alternate - interior angles) and ∠BCA = ∠DAC (alternate - interior angles).

Step3: Identify common side

AC = AC (reflexive property of congruence).

Step4: Prove triangle congruence

By the Angle - Side - Angle (ASA) congruence criterion, △ABC≅△CDA.

Step5: Use congruent - triangle property

Since △ABC≅△CDA, AB = CD and BC = DA (corresponding parts of congruent triangles are congruent).

Answer:

AB = CD and BC = DA are proved as above.