1. Preview
Warm Up
California Standards
Lesson Presentation

2. 1. Draw two points. Label one point A and the other point B.
Warm Up
1. Draw two points. Label one point A and the other point B.
2. Draw a line through points A and B.
3. Draw a ray with A as an endpoint and C as a point on the ray.
4. Name all the rays in your drawing. C
AB, BA, and AC A B

3. Preparation for MG2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.
Also covered: Prep for MG2.3
California
Standards

4. Vocabulary angle vertex acute angle right angle obtuse angle
straight angle

5. An angle is formed by two rays with a common endpoint, called the vertex. An angle can be named by its vertex or by its vertex and a point from each ray. The middle point in the name should always be the vertex.
Angles are measured in degrees. Use the symbol ° to show degrees.

6. Additional Example 1: Measuring an Angle with a Protractor
Use a protractor to measure the angle. G H F
Place the center point of the protractor on the vertex of the angle.

7. Additional Example 1 Continued
Use a protractor to measure the angle. G H F
Place the protractor so that ray GH passes through the 0° mark.

8. Additional Example 1 Continued
Use a protractor to measure the angle. G H F
Using the scale that starts with 0° along ray GH, read the measure where ray GF crosses.

9. Reading Math
mFGH is read “the measure of angle FGH.”

10. Additional Example 1 Continued
Use a protractor to measure the angle. G H F
The measure of FGH is 120°. Write this as mFGH = 120°.

11. Check It Out! Example 1
Use a protractor to measure the angle. G I H
Place the center point of the protractor on the vertex of the angle.

12. Check It Out! Example 1 Continued
Use a protractor to measure the angle. G I H
Place the protractor so that ray HI passes through the 0° mark.

13. Check It Out! Example 1 Continued
Use a protractor to measure the angle. G I H
Using the scale that starts with 0° along ray HI, read the measure where ray HG crosses.

14. Check It Out! Example 1 Continued
Use a protractor to measure the angle. G I H
The measure of GHI is 70°. Write this as mGHI = 70°.

15. Additional Example 2: Drawing an Angle with a Protractor
Use a protractor to draw an angle that measures 80°.
Draw a ray on a sheet of paper.

16. Additional Example 2 Continued
Use a protractor to draw an angle that measures 80°.
Place the center point of the protractor on the endpoint of the ray.
Place the protractor so that the ray passes through the 0° mark.

17. Additional Example 2 Continued
Use a protractor to draw an angle that measures 80°.
Make a mark at 80° above the scale on the protractor.
Use a straightedge to draw a ray from the endpoint of the first ray through the mark you made at 80°.

18. Use a protractor to draw an angle that measures 45°.
Check It Out! Example 2
Use a protractor to draw an angle that measures 45°.
Draw a ray on a sheet of paper.

19. Use a protractor to draw an angle that measures 45°.
Check It Out! Example 2 Continued
Use a protractor to draw an angle that measures 45°.
Place the center point of the protractor on the endpoint of the ray.
Place the protractor so that the ray passes through the 0° mark.

20. Use a protractor to draw an angle that measures 45°.
Check It Out! Example 2 Continued
Use a protractor to draw an angle that measures 45°.
Make a mark at 45° above the scale on the protractor.
Use a straightedge to draw a ray from the endpoint of the first ray through the mark you made at 45°.

21. An acute angle measures less than 90°.
A right angle measures exactly 90°.
Right angles are usually marked with a symbol.
Reading Math

22. An obtuse angle measures more than 90° and less than 180°.
A straight angle measures exactly 180°.

23. Additional Example 3: Classifying Angles
Classify each angle as acute, right, obtuse, or straight.
A. B.
The angle measures less than 90°, so it is an acute angle.
The angle measures exactly 90°, so it is a right angle.

24. The angle measures less than 90°, so it is an acute angle.
Check It Out! Example 3
Classify each angle as acute, right, obtuse, or straight.
A. B.
The angle measures less than 90°, so it is an acute angle.
The angle measures exactly 180°, so it is a straight angle.

25. Additional Example 4: Application
A welder used this piece of metal on his project. Classify X, Y, and Z.
X right
The angle is marked as a right angle.
Y obtuse
The angle measures more than 90° and less than 180°.
Z acute
The angle measures less than 90°.

26. The angle measures more than 90° and less than 180°.
Check It Out! Example 4
A metal jeweler used this piece of metal on her project. Classify A, B, and D. A D B C
A obtuse
The angle measures more than 90° and less than 180°.
B acute
The angle measures less than 90°.
D right
The angle is marked as a right angle.

27. Lesson Quiz
Use a protractor to draw an angle with the given measure. Tell what type of angle it is.
1. 140°
2. 20°
3. Draw a right angle.
4. Is the angle shown closer to 30° or 120°?
Check student drawings; obtuse
Check student drawings: acute
30°