Question

B. Describe the angle relationships formed when parallel lines are cut by a transversal.

Answer 1

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary . ... When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles

Answer 2

1) The corresponding angles are equal.(∠1 = ∠5), (∠2 = ∠6), (∠3 = ∠7), (∠4 = ∠8)

2) Alternative interior angles are equal. (∠3 = ∠5, and ∠4 = ∠6)

3) The vertical opposite angles are equal. (∠1 = ∠3), (∠2 = ∠4), (∠5 = ∠7), (∠6 = ∠8)

4) Alternative exterior angles are equal. (∠1 = ∠7), (∠2 = ∠8)

5) The pair of interior angle on the same side add upto 180 degrees.

Explanation:

When parallel lines are cut by a transversal, we get 8 angles as shown in the figure.

It holds true the following relationship.

1) The corresponding angles are equal.(∠1 = ∠5), (∠2 = ∠6), (∠3 = ∠7), (∠4 = ∠8)

2) Alternative interior angles are equal. (∠3 = ∠5, and ∠4 = ∠6)

3) The vertical opposite angles are equal. (∠1 = ∠3), (∠2 = ∠4), (∠5 = ∠7), (∠6 = ∠8)

4) Alternative exterior angles are equal. (∠1 = ∠7), (∠2 = ∠8)

5) The pair of interior angle on the same side add upto 180 degrees.