Big Ideas Math: Modeling Real Life, Grade 8
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Big Ideas Math: Modeling Real Life, Grade 8 View details
1. Parallel Lines and Transversals
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Exercise 7 Page 108

What can you notice about the measures of the angles created by the intersection of the lines?

No, lines a and b are not parallel.

Practice makes perfect

We want to determine whether lines a and b are parallel. Let's take a look at the given graph.

Graph with protractor
We will use a protractor to measure the angles created by the transversal t. Let's start with line a.
Graph with protractor

The measure of the angle formed by the intersection of lines a and t is about 120^(∘). Let's do the same for line b.

Graph with protractor

The measure of the angle formed by the intersection of lines b and t is about 115^(∘).

Graph with protractor
We can see that the measures of the corresponding angles formed by both intersections are not equal. This means that lines a and b are not parallel.

Extra

Types of Angle Pairs

Let's review what we know about different types of angle pairs. We will use the graph below as an example.

Now we can list the different types of angle pairs together with their definitions.

Pairs of Angles
Type Definition Example
Supplementary Angles Together, they form a straight line and their measures add up to 180^(∘). ∠ 1 and ∠ 3
Vertical Angles They lie on the opposite sides of the point of intersection of two lines. ∠ 1 and ∠ 4
Corresponding Angles They lie in corresponding positions on the same side of the transversal. ∠ 3 and ∠ 7
Alternate Interior Angles They lie between the two lines on opposite sides of the transversal. ∠ 4 and ∠ 5
Alternate Exterior Angles They lie outside the two lines on opposite sides of the transversal. ∠ 2 and ∠ 7