Question

Complete the proof to show that ABCD is a parallelogram. BCllAD and CDllBA because the___________. therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.

Answer 1

Answer: SECOND OPTION.

Step-by-step explanation:

By definition, the slopes of parallel lines are equal.

The slope of a line can be found applying this procedure:

1. Choose two points on the line.

2. Substitute the coordinates of each point chosen into the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

3. Evaluate in order to find the slope.

A parallelogram is a quadrilateral whose opposite sides are parallel and have equal length.

Let's assume that  that BC and AD have equal length and CD and BA have equal length. Then:

1. If you calculate the slope of BC and the slope of AD and they are equal, then BC and AD are parallel.

2. If find the slope of CD and the slope of BA and they are equal, then CD and BA are parallel.

Therefore ABCD is a parallelogram.