Question

How do I prove that BCEF is a parallelogram?

a) Show that opposite sides are parallel.
b) Show that opposite angles are congruent.
c) Demonstrate that one pair of opposite sides has equal length.
d) Prove that one pair of opposite angles is supplementary.

Answer 1

To prove that BCEF is a parallelogram, you need to show that it satisfies all the properties of a parallelogram, including parallel sides, congruent angles, and equal opposite sides. You can choose any of these properties and demonstrate that it holds true for BCEF.

Step-by-step explanation:

To prove that BCEF is a parallelogram, we need to show that it satisfies all the properties of a parallelogram, which are:

1. Opposite sides are parallel.
2. Opposite angles are congruent.
3. One pair of opposite sides has equal length.
4. One pair of opposite angles is supplementary.

To prove that BCEF is a parallelogram, you can choose any of these properties and demonstrate that it holds true for BCEF. For example, you can show that opposite sides BC and EF are parallel by demonstrating that their slopes are equal. You can also show that opposite angles B and E are congruent by proving that they are alternate interior angles formed by a transversal intersecting parallel lines.