Question

6. В четырехугольнике ABCD AB = DC и BAC = ACD. Докажите, что AD = BC.

Answer 1

Given Information:

We are given a quadrilateral ABCD, where AB = DC and ∠BAC = ∠ACD.

To Prove:

We need to prove that AD = BC.

Proof:

To prove that AD = BC, we will use the given information and the properties of quadrilaterals.

Since AB = DC, we can conclude that triangle ABC is congruent to triangle CDA by the Side-Side-Side (SSS) congruence criterion.

Also, since ∠BAC = ∠ACD, we can conclude that triangle ABC is congruent to triangle CDA by the Angle-Side-Angle (ASA) congruence criterion.

Therefore, triangle ABC is congruent to triangle CDA by both the SSS and ASA congruence criteria.

By the congruence of triangles ABC and CDA, we can conclude that AD = BC.

Hence, we have proved that AD = BC.

Note: The proof provided above is based on the given information and the properties of quadrilaterals.