Question

Given: AD = BC and AD || BC


Prove: ABCD is a parallelogram.

Answer 1

To prove that ABCD is a parallelogram, we need to show that opposite sides are equal in length and parallel to each other. Given that AD = BC and AD || BC, we can use the properties of parallel lines and transversals to prove this.

Step-by-step explanation:

To prove that ABCD is a parallelogram, we need to show that opposite sides are equal in length and parallel to each other. Given that AD = BC and AD || BC, we can use the properties of parallel lines and transversals to prove this.

First, since AD || BC, we can conclude that angle A is congruent to angle C (alternate interior angles). Similarly, angle D is congruent to angle B (alternate interior angles).

Next, using the given information AD = BC, we can show that opposite sides AB and CD are equal in length. By the Transitive Property of Equality, we can say that AD = AB + BD. Since AD = BC and AB + BD = BC, it follows that AB = CD.

Finally, to show that AB || CD, we can use the Consecutive Interior Angles Theorem. Since angle A is congruent to angle C and angle D is congruent to angle B, the pairs of angles on the same side of the transversal are congruent. This implies that AB || CD.

Answer 2

ABCD is a parallelogram

Step-by-step explanation:

Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a

parallelogram. Statements Reasons 1. AD ≅ BC; AD ∥ BC

1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2.

definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3.

alternate interior angles are congruent 4. AC ≅ AC 4.

reflexive property 5. △CAD ≅ △ACB 5. SAS congruency

theorem 6. AB ≅ CD 6. ? 7. ABCD is a parallelogram 7.