In this topic, you will apply your reasoning skills and your knowledge of angle relationships to prove that lines are parallel. You will discover how direct proofs—in the form of two-column proofs, paragraph proofs, and flow proofs—can be used to help you explain your reasoning. You will also learn how to use your knowledge of angle relationships to set up and solve algebraic equations in order to prove that lines are parallel.
Essential Questions
- How can you prove lines are parallel when given angle measurements expressed numerically or algebraically?
- How can you use deductive proofs to prove lines are parallel?
Warm-Up
Look at the diagram provided. You are able to interpret the markings and determine that the transversal is intersecting two parallel lines. However, you probably noticed that ∠1 and ∠2 do not make up any of the angle pairs that are formed by a transversal intersecting parallel lines. In other words, ∠1 and ∠2 are not corresponding angles, nor alternate interior angles, etc. If you knew one of the angle measures, could you determine the measure of the other angle without having to determine each of the other angle measures?
