1-4 Angle Measure

1. 1-4 Angle Measure What is a protractor and why is it used?

2. You measured line segments. • Measure and classify angles. • Identify and use congruent angles and the bisector of an angle.

3. New Vocabulary • degree • right angle • acute angle • obtuse angle • angle bisector • ray • opposite rays • angle • side • vertex • interior • exterior

4. Vocabulary Ray part of a line. It has one endpoint and extends infinitely in one direction. D O G To name a ray, start with the endpoint followed by another point on the ray. P O N M

5. Vocabulary Opposite rays are two rays sharing a common end point.

6. Vocabulary Angle is formed by two rays (that are not collinear) with a common endpoint or vertex. The two rays are the sides of the angle. An angle is named by using three different letters. The vertex letter is always in the middle. When there are no other angles around, the angle may be named by the letter at the vertex. R side S vertex side T

7. Vocabulary An angle divides a plane into three distinctive parts: On the angle In the interior of the angle In the exterior of the angle W R side X S vertex side T

8. Name the angle in four ways. A 1 B C

9. Measuring Angles Angles have different sizes and are usually measured in degrees. Angles measure between 0° and 180°. The measure of an angle is written The size of of an angle is not the same thing as the angle itself.

10. Protractor

11. Using a Protractor to measure

12. Using a protractor to measure

13. More Vocabulary

14. Measure and Classify Angles A. Measure TYV and classify it as right, acute, or obtuse. Answer:mTYV = 90, so TYV is a right angle.

15. Measure and Classify Angles Answer: 180 > mWYT > 90, so WYT is an obtuse angle.

16. Measure and Classify Angles

17. Example 3 INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find mGBH and mHCI if GBH  HCI, mGBH = 2x + 5, and mHCI =3x – 10.

18. Example 3 Step 1 Solve for x. GBH  HCI Given mGBH = mHCI Definition of congruent angles 2x + 5 = 3x – 10 Substitution 2x + 15 = 3x Add 10 to each side. 15 = x Subtract 2x from each side.

19. . Example 3 Step 2 Use the value of x to find the measure of either angle. Answer:mGBH = 35, mHCI = 35

20. Construction: Copy an Angle • Draw an angle to copy. • Draw a ray for your construction area. • Put the sharp tip of your compass on the vertex (point) of the angle to copy. • Draw an arc crossing both sides of the angle • Without changing the size of your compass, put the point on the end point of your ray. Make an arc. • Go back to the angle and put each point of your compass on the spot that the arc crosses the sides of the angle.

21. Copy an Angle 7. Without moving the size of the compass, put the pointed tip on the spot where the arc crosses the ray. Make a mark that crosses the arc. 8. Connect the endpoint and the curved “X” to finish your constructed angle. You have constructed congruent angles!!

22. Construction: Bisect an Angle • Draw an angle on your paper. • Put the point of your compass on the vertex and draw a large arc. • Without moving the compass, put the point on the bottom side where the arc crossed the side. Make a mark in the interior of the angle. • Turn the compass and put the point on the other side where the arc crosses the side. Make a mark in the interior of the angle crossing the other mark. • Draw a ray connecting the vertex and the “X”. You have bisected an angle!!

23. Assignment 1-4 p. 41, 13-41 odd