Question

write proof of triangle ABD congruent to triangle DCA, you may write a paragraph proof, a flowchart proof, or a two column proof. given AC is parallel to BD ; CD is parallel to AB. prove triangle ABD is congruent to DCA

Answer 1

By using the properties of parallel lines and the ASA Postulate, we can prove that triangle ABD is congruent to triangle DCA due to congruent alternate interior angles and a shared side.

Step-by-step explanation:

We are given that AC is parallel to BD, and CD is parallel to AB. Since AC is parallel to BD, and they are both intersected by AD, the alternate interior angles formed are congruent. That means ∠CAD is congruent to ∠BDA. Similarly, since CD is parallel to AB, and they are intersected by AD, the alternate interior angles formed are congruent as well. Hence, ∠ACD is congruent to ∠BAD. By the Reflexive Property of Equality, AD is congruent to AD. With two pairs of congruent angles and a common side, △ABD is congruent to △DCA by the ASA Postulate (Angle-Side-Angle).