Question

Fred states that if e, is parallel to , and & is parallel to , then it follows that h, is parallel to l3. Is Fred right? Show your answer using a diagram.

Answer 1

Yes, Fred is correct because if ℓ
`_1` is parallel to ℓ
`_2`, and ℓ
`_2` is parallel to ℓ
`_3`, then it follows that ℓ
`_1` is parallel to ℓ
`_3` based on corresponding angles theorem.

In Mathematics and Geometry, corresponding angles theorem is a theorem which states that corresponding angles are always congruent when the transversal intersects two or more parallel lines.

By applying corresponding angles theorem to the two parallel lines ℓ
`_1` and ℓ
`_2` cut through by transerval t, we have the following congruent angles:

m∠1 ≅ m∠2

By applying corresponding angles theorem to the two parallel lines ℓ
`_1` and ℓ
`_3` cut through by transerval t, we have the following congruent angles:

m∠1 ≅ m∠3

In this context, we can logically conclude that Fred's postulate is correct.

Complete Question:

Fred states that if ℓ
`_1` is parallel to ℓ
`_2`, and ℓ
`_2` is parallel to ℓ
`_3`, then it follows that ℓ
`_1` is parallel to ℓ
`_3`. Is Fred right? Show your answer using a diagram.