Stan knows that segment AB∥segment CD. He wants to use the definition of a parallelogram to prove that quadrilateral ABCD is a parallelogram. Which equation can he use?

Step-by-step explanation:

Given

See attachment for parallelogram

Required

Proof that ABCD is a parallelogram

We know that opposite sides are equal and parallel.

First, we calculate the slope of BC

So, we have:

Next, the slope of AD using:

So, we have:

For ABCD to be a parallelogram; then:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47