Question

Edge 2020: 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 parallel and congruent. Given that AD = BC and AD || BC, we can use the properties of parallel lines to prove these conditions.

Step-by-step explanation:

To prove that ABCD is a parallelogram, we need to show that opposite sides are parallel and congruent. Given that AD = BC and AD || BC, we can use the properties of parallel lines to prove these conditions.

1. Opposite sides are parallel:

• Since AD || BC, we can conclude that AB || CD (by the transitive property of parallel lines).

2. Opposite sides are congruent:

• Since AD = BC, we can conclude that AB = CD (by the definition of congruent segments).

Therefore, with both conditions met, we can conclude that ABCD is a parallelogram.