## Think About Angles

## Opening

# Think About Angles

- Describe the angle(s) in this figure.
- Discuss your ideas with your class.

- Describe the angle(s) in this figure.
- Discuss your ideas with your class.

Discuss the following with your classmates.

- ∠
*ABD*and ∠*CBD*are*adjacent angles.*Adjacent angles share a vertex and a side. - ∠
*ABD*and ∠*CBD*are also*supplementary angles*. The measures of supplementary angles add up to 180°. - ∠
*ABC*is a straight angle.

Explore the relationships between adjacent, supplementary, complementary, and vertical angles.

- Start with a sheet of paper. Fold the left edge over the right edge at a slant. Unfold. Fold the top edge over the bottom edge at a slant. Unfold.
- Using your protractor, measure each of the four angles created by the intersection of the folds. Write the angle measures on the paper. What do you notice?
- Measure each of the angles formed by the folds and the edges of the paper. What do you notice?

Use the Angles Sketch interactive to explore each set of angles:

- The line and ray forming a straight angle
- The intersecting lines
- The rays forming a right angle

Answer the following questions.

- Write at least one observation about each set of angles 1
**–**8. - Can you make angles 1 and 2 congruent? If so, what type of angle did they become?
- Can you make angles 3, 4, 5, and 6 congruent? If so, what type of angle did they become?

INTERACTIVE: Angles Sketch

Try adding different angles together. What is their sum? Which angles are congruent?

Summarize the observations you made about angle relationships and the sums of angles.

- Two complementary angles like ∠7 and ∠8 form a 90° angle. Can you make one angle 5 times the measure of the other angle?

Take notes about your classmates’ observations concerning angle relationships and the sum of angles.

As your classmates present, ask questions such as:

- Which angles were congruent? Why do you think they were congruent?
- What was the sum of the angles?

**Read and Discuss**

*Supplementary angles*are two angles with measures that add up to 180°. Two supplementary angles together form a straight angle.- In Figure 2, ∠
*c*and ∠*d*are supplementary angles.

- In Figure 2, ∠
*Complementary angles*are angles with measures that add up to 90°. Two complementary angles together form a right angle.- In Figure 1, ∠
*x*and ∠*y*are*complementary angles.*

- In Figure 1, ∠
- Two intersecting lines create four angles. Each pair of equal angles are vertically opposite angles or
*vertical angles*.- In Figure 2, ∠
*a*and ∠*c*are*vertical angles.*

- In Figure 2, ∠
*Adjacent angles*are angles that are next to each other; they share a vertex and a side.- In Figure 2, ∠
*a*and ∠*d*are*adjacent angles.*

- In Figure 2, ∠

Can you:

- Explain when adjacent angles are supplementary?
- Explain what is true of vertical angles?
- Describe the angle formed by two angles that are complementary and adjacent?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**I think complementary and supplementary angles are similar in these ways… and different in these ways …**