Welcome to Interactive Chalkboard

1. Welcome to Interactive Chalkboard 1.4 Angle Measures

2. Objectives: • How to label, measure, and classify angles • Identifying and using congruent angles • Creating and utilizing an angle bisector

3. Rays • A ray • is part of a line which has one endpoint and extends infinitely in one direction. • named stating the endpoint first and then any other point on the ray.

4. Labeling Rays • We could label this ray as AB, AC, or AD but not CA. D C B A

5. More about Rays • If you choose a point on a line, that point determines exactly two rays called opposite rays. P Q R QP and QR are opposite rays.

6. Angles and Their Parts • An angleis formed by two noncollinear rays that have a common endpoint. • the rays are called sides • common endpoint is the vertex. B Side AB Side AC A C Vertex A

7. Labeling Angles • We label angles any of the following ways: BAC, CAB, A, or 1 B 1 A C

8. More about Angles • An angle divides a plane into three distinct parts. Points A, B, and C lie on the angle. Points D and E line in the interior of the angle. Points F and G lie in the exteriorof the angle. B D F E 1 A C G

9. Example 1a: Name all angles that have B as a vertex. Answer:5, 6, 7, and ABG

10. Answer: and or are the sides of 5. Example 1b: Name the sides of 5.

11. Example 1c: Write another name for 6. Answer:EBD, FBD, DBF, and DBE are other names for 6.

12. a. Name all angles that have X as a vertex. b. Name the sides of 3. Answer: c. Write another name for 3. Your Turn: Answer:1, 2, 3, and RXB or RXN Answer:AXB, AXN, NXA, BXA

13. Measuring Angles • To measure an angle we use a protractor. • Place the center of the protractor on the vertex and one side of the angle on either side of the 0° line of the protractor. • The protractor will have two scales running from 0° to 180° in opposite directions. • Read the measure of the angle by viewing the alignment of the other side of the angle with the proper scale.

14. Classifying Angles • There are four types of angles. Acute angles measure < 90°. Right angles measure 90°. Obtuse angles measure > 90° but < 180°. Straightangles measure 180°.

15. Answer: is a right angle. Example 2a: Measure TYV and classify it as right, acute, or obtuse. TYV is marked with a right angle symbol, so measuring is not necessary.

16. Use a protractor to find that . Answer: > is an obtuse angle. Example 2b: Measure WYT and classify it as right, acute, or obtuse.

17. Use a protractor to find that m . Answer: is an acute angle. Example 2c: Measure TYU and classify it as right, acute, or obtuse.

18. Measure each angle named and classify it as right, acute, or obtuse. a.CZD b.CZE c.DZX Your Turn: Answer: 150, obtuse Answer: 90, right Answer: 30, acute

19. Congruent Angles • Just as segments that have equal measures are congruent, angles that have the same measures are congruent. To label angles congruent we use tic marks just like we used for segments. BAC  YXZ C Z X A B Y

20. More about Congruent Angles • A ray that divides an angle into two congruent angles is called an angle bisector. If AD bisects BAC then BAD is congruent to CAD. B D A C

21. 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. Example 3:

22. Example 3: Given Definition of congruent angles Substitution Add 10 to each side. Subtract 2x from each side.

23. Since . Answer: Both measure 35. Example 3: Use the value of x to find the measure of one angle. Given or 35 Simplify.

24. SIGNS A railroad crossing sign forms congruent angles. In the figure, WVX ZVY. If mWVX 7a + 13and mZVY 10a – 20, find the actual measurements of WVXandZVY. Answer: Your Turn:

25. Assignment: • Geometry: Pg. 34 – 35, #12 - 37 • Pre-AP Geometry: Pg. 34 – 35, #12 – 39, 45 - 48