Question

Given:

AB | | CD
AD | | CB

Prove :
AD = CB

Which of the following statements would complete the proof?

<1 = <2 and <3 = <4

<1 = <3 and <2 = <4

<1 = <4 and <2 = <3

Answer 1

Third one

<1 = <4 and <2 = <3

Explanation:

When two parallel lines form a Z shape, we call the angles at the vertices of Z to be alternate interior angles, which are equal

Answer 2

C. <1 = <4 and <2 = <3

Explanation:

When two lines are parallel, the angles that are formed have certain properties.

There is a pair of angles in particular called alternate interior angles; these are basically the angles within the parallel lines. They are always equal to each other. Here, we will use the fact that AB || CD.

AB and CD create the angles 1 and 4. Angles 1 and 4 are alternate interior angles, so they are equal: <1 = <4

Similarly, we need to use the fact that AD || CB. These two parallel lines create the angles 2 and 3. We can see that because these two angles are "within"/formed by the parallel lines, they are alternate interior so they equal: <2 = <3.

Thus, the answer is C.

Hope this helps! (Sorry about the delay!!)