1. 1.2 FINDING ANGLES Geometry

2. IS THE ANGLE BETWEEN THE HOUR AND MINUTE HAND THE SAME ON BOTH CLOCKS? EXPLAIN YOUR ANSWER AND THEN EXPLAIN HOW YOU WOULD PROVE IT. Clock AClock B DO NOW:

3. Protractor A device used to measure angles.

4. ARE THESE PROTRACTOS LINED UP CORRECTLY?

5. Look for the upside down ‘T’ in the middle of the straight line on your protractor. In this protractor look for the hole in the center. These spots need to be exactly on the vertex of your angle. No!! The angles must be lined up properly.

6. We also need to remember to line up the base One side of the angle must be lined up with the base of the protractor. It doesn’t matter which side.

7. WHAT IS THE ANGLE MEASURE? This angle measures 35°. The side of the angle passes over 2 measurements: 145° and 35°. Which one is correct??

8. CAN YOU DRAW ME A 60 DEGREE ANGLE? Now on your own, draw any angle you wish and measure it! Now can you draw me a bisecting ray of that angle we just made? What do we notice?

9. What do you see??

10. Pool Table Problems The incoming angle equals the outgoing angle. What do you notice about the outgoing and incoming angles?

11. INDIVIDUALLY: STEP 1 AND STEP 2 Then we will share with our group.

12. Pool Table Problems If I was to hit the white ball on the path given, which letter would it hit after I hit the cushion wall?

13. Pool Table Problems Which point should I hit I could hit the 8-ball exactly? W? X? or Y?

14. Pool Table Problems - Notes Where do we aim on the bottom cushion so white hits blue?

15. Where do we aim on the top cushion so white hits blue?

16. Where do we aim on the left cushion so white hits blue?

17. Where do we aim on the left cushion so white hits the bottom cushion and then hits blue?

18. A revolution is an angle that equals exactly 360º. Full Revolution

19. NAMING ANGLES An angle is made of two rays. We label the angle with three upper case letters. X Y Z Y is called the Vertex Naming the Angle  XYZ  ZYX  Y Y

20. Use a single letter to name the angle. A B C BB

21. NAMING ANGLES Use a single letter to name the angle. P Q R QQ

22. E G F GG

23. Use three letters to name the angle. L N M   LNM

24. NAMING ANGLES Use three letters to name the angle. R S T   RST

25. Use three letters to name the angle. E G F   EGF

26. Reflex Angle A reflex angle is greater than 180º and less than 360º. It represents the largest amount of rotation.

27. Angle Bisector lineline or line segment that divides the angle into two equal parts (marked by slash marks).line segment.D.D