Content
Using Angle Relationships to Prove Lines Are Parallel

Paragraph Proof

In your study of geometry, you will examine and develop many kinds of proofs. A proof is any kind of valid argument that shows how a statement is true. A paragraph proof is simply a proof that is written in paragraph form. Below is an example of a paragraph proof.

Problem: Given the diagram below, determine which pair of lines are parallel. figure 1 Response: Take a look at the correct answer and explanation below. figure 2 The diagram shows the 75° angle formed by the intersection of line AD and line DC and the 105° angle formed by the intersection of line BC and line DC. These angles are same-side interior angles. If same-side interior angles are supplementary, then a transversal intersected two parallel lines. Therefore, you can conclude that line AD is parallel to line BC.

 

Properties

When using deductive reasoning to complete direct proofs, you will apply various definitions, postulates, theorems, and properties. Two properties that you may find useful are given below.

Transitive Property of Congruence

Given: ∠1, ∠2, and ∠3
If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3.

Note: This property can be applied to relationships between congruent segments and congruent figures.

Substitution Property of Equality

If two values are equal, then one can replace another in any expression.

 

Using Angle Relationships to Prove Lines Are Parallel

Using Angle Relationships to Prove Lines Are Parallel Video

In this video, you will learn how to prove two lines are parallel by using two-column proofs. You will also learn how to prove that two lines are parallel when given angle measurements expressed numerically or algebraically. Click the player button to begin.

View a transcript of this video.

Proving Parallel Lines in a Two-Column Proof

Proving Parallel Lines in a Two-Column Proof interactivity

In this interactivity, you will view a figure along with given information needed to prove the lines are parallel. Consider the provided statements of the two-column proof and determine what the reasons are.

View a printable version of this interactivity.

 

Using Angle Relationships to Prove Lines Are Parallel Review

Using Angle Relationships to Prove Lines Are Parallel Review interactivity

warm-up icon Now that you have learned about using angle relationships to prove lines are parallel, review your knowledge in this interactivity. Click the player button to get started.