Question

Transversal t cuts parallel lines r and s as shown in the diagram. Which theorem does the diagram illustrate?

A) Alternate Interior Angles Theorem



B) Alternate Exterior Angles Theorem



C) Same-Side Interior Angles Theorem


D) Corresponding Angles Theorem

Answer 1

B alternate exterior angles

Answer 2

The correct option is B. Alternate Exterior angles theorem

Explanation:

Let name the marked angles in the figure as x and y

Given that : x = y

So, to state which theorem does the diagram illustrate, we first need to find the relation between the angles x and y

Alternate interior angles : The angles which lie interior to the parallel sides but on the opposite side of the transversal.

But x and y lie exterior to the parallel lines, So this option is rejected.

Alternate exterior angles : The angles which lie exterior to the parallel sides but on the opposite side of the transversal.

But x and y lie exterior to the parallel lines, So this option is correct.

Same side interior angles theorem : This theorem states that the sum of same side interior angles in 180.

So it can't be said angle x = angle y by using this theorem. So, this option is rejected

Corresponding angles theorem : The angle which lie at same relative position of the transversal.

But, angle x and angle y lie on the opposite side. So, this option is rejected

Hence, The correct option is B. Alternate Exterior angles theorem