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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

5. Angles and Parallel Lines

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Exercise 31 Page 312

Analyze which lines form the angles and find out what they are called. Then use the appropriate theorem or postulate to find the relationship between the angles.

Congruent, alternate interior angles.

Practice makes perfect

We are given a diagram representing the side of a industrial shelving. Since it needs additional support, some transverse members are added. In this exercise we are asked to find the relationship between angles ∠ 1 and ∠ 8. Let's find these angles on the given diagram.

In order to find the relationship between the angles ∠ 1 and ∠ 8, we should know which lines form these two angles. Let's use our diagram to identify these lines. We will name the lines so the following explanations will be easier.

Note that the lines a and b are parallel. Therefore, angles ∠ 1 and ∠ 8 are interior angles of the parallel lines a and b. Also, they are alternate angles of the transversal c. Therefore, ∠ 1 and ∠ 8 are alternate interior angles. We can use Alternate Interior Angles Theorem to determine the relationship between them.

Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

From this theorem we can conclude that angles ∠ 1 and ∠ 8 are congruent angles, which means that they have the same measures.

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Exercises p.311-314