Glencoe Math: Course 3, Volume 2
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Glencoe Math: Course 3, Volume 2 View details
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Exercise 22 Page 377

We are given the following diagram.

The glass pyramid

We want to determine which of the given statements is not true concerning and Let's analyze the statements one at a time.

Statement F

First, we will consider statement F.

and are obtuse angles.

Recall that obtuse angles are angles that measure more than but less than Let's look at and

The glass pyramid

We can see that and are right angles. Since these angles have a measure of they are not obtuse. Therefore, statement F is not true.

Statement G

Now we will analyze statement G.

and are vertical angles.

When two lines or line segments intersect, vertical angles are formed on opposite sides of the point of intersection. To check whether and are vertical, let's take another look at the diagram.

The glass pyramid

Notice that and are on opposite sides of the point of intersection of two lines. This means that these angles are vertical, so statement G is true.

Statement H

Next, we will consider statement H.

and are alternate interior angles.

Notice that in the diagram, we have two parallel lines that are cut by a transversal. Recall that alternate interior angles are interior angles that lie on opposite sides of the transversal. Looking at the diagram, we can determine whether and are alternate interior angles.

The glass pyramid

Indeed, and are interior angles that lie on opposite sides of the transversal. Therefore, these angles are alternate interior angles, and statement H is true.

Statement I

Finally, we will analyze statement I.

and are congruent.

Since statement G is true, we know that and are vertical angles. Recall that vertical angles are always congruent. This means that and are congruent and statement I is also true.

Conclusion

We found that only statement F is not true.