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1.4 A N G L E S

1.4 A N G L E S. An angle is a geometric figure that consists of two rays that share a common endpoint. The two rays are called the sides of the angle. The common endpoint of the two rays is called the vertex of the angle. Naming an Angle.

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1.4 A N G L E S

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  1. 1.4 ANGLES

  2. An angle is a geometric figure that consists of two rays that share a common endpoint. • The two rays are called the sides of the angle. The common endpoint of the two rays is called the vertex of the angle

  3. Naming an Angle • Every angle is named by three letters. The middle letter is the name of the vertex. • Another way to name an angle is by the angle’s vertex. • Look at the top of p.17 for other ways we can name angles L ABC or LCBA OR L B A Angle (ABC) B C

  4. This confusing… • Can we use just the vertex to name these angles? A B C D

  5. How many angles are there? A 1 B 3 C 2 D

  6. Angle Measurements • We measure the size of an angle using degrees. • We measure the size of an angle using a protractor HOW DO WE USE A PROTRACTOR?

  7. Right Angle A right angle is an angle measuring exactly 90 degrees. This angle measures 90 degrees. It is a right angle. You use a protractor to measure angles.

  8. This angle is less than 90 degrees. It is called an acute angle. Acute Angle An acute angle is an angle measuring between 0 and 90 degrees. “Ohhhh look at the a cute little angle that is…..”

  9. This angle is greater than 90 degrees. It is called an obtuse angle. Obtuse Angle An obtuse angle is an angle measuring between 90 and 180 degrees.

  10. Straight Angle • A straight angle is 180 degrees. A straight angle Is a straight _____?

  11. GAME TIME! • The object of the game is to be the first to raise your hand and correctly name what type of angle you see. • The correct answer will be on the following slide!! • Good luck!

  12. AcuteAngle

  13. ObtuseAngle

  14. RightAngle

  15. StraightAngle

  16. GREATJOB!!

  17. Protractor Postulate (pg.18) • Read it on your own • It basically tells us that we can use our protractor to line up and measure the degrees of angles (just as we lined up the ruler to measure length) • It also discusses absolute value, just like with the number line

  18. Angle Addition Postulate • If point B lies in the interior of  AOC, • then m  AOB + m  BOC = m  AOC. • What is the interior of an angle? If  AOC is a straight angle and B is any point not on AC, then m  AOB + m  BOC = 180. Why does it add up to 180?

  19. Congruent Angles • Angles that have equal measure

  20. Adjacent Angles Two angles in a plane that have.. • a common vertex • and a common side but no common interior points. Common Side No Common interior Points Common Vertex

  21. Duplex Common Roof No Common Things Common Wall

  22. Remote time

  23. T – AdjacentF – Not adjacent 2 1

  24. T – AdjacentF – Not adjacent 2 1

  25. T – AdjacentF – Not adjacent 1 2

  26. T – AdjacentF – Not adjacent 1 2

  27. T – AdjacentF – Not adjacent 1 2

  28. Bisector of a segment A line, segment, ray or plane that intersects the segment at its midpoint. B 3 3 P A Something that is going to cut directly through the midpoint

  29. Bisector of an Angle • The ray that divides the angle into two congruent adjacent angles (pg 19) B BX bisects L ABC Name the two congruent angles C X A

  30. Assumptions • There are certain things that you can conclude from a diagram and others that you can’t.

  31. Group Problem A D B E C

  32. What can you Assume? A D Be Careful B E C

  33. What you can Assume? • All points shown are coplanar • AB, BD, and BE intersect at B. • A, B, C are collinear • B is between A and C • ABC is a straight angle • D is in the interior of ABE • ABD and DBE are adjacent angles. A D B E C

  34. What you can’t Assume? A • AB BC • ABD  DBE • CBE is a right angle D B E C

  35. Arc marks – indicate congruent angles A D Tick marks – indicate congruent segments B E Indicates a 90 degree angle Marks are used to indicate conclusions about size in a diagram. C

  36. Lessons Learned… • Don’t Assume ! • Follow this rule: You can draw conclusions about position, but not about size. • Use markings to help you find out information about the diagram

  37. B 4 2 3 1 9 8 7 6 5 C A E D Practice on the White Boards

  38. B 4 2 3 1 9 8 7 6 5 C A E D Name the vertex of  3

  39. B 4 2 3 1 9 8 7 6 5 C A E D Name the right angle

  40. B 4 2 3 1 9 8 7 6 5 C A E D State another name for 1

  41. B 4 2 3 1 9 8 7 6 5 C A E D State another name for 6

  42. B 4 2 3 1 9 8 7 6 5 C A E D State another name for 3

  43. B 4 2 3 1 9 8 7 6 5 C A E D State another name for 4

  44. B 4 2 3 1 9 8 7 6 5 C A E D State another name for 7

  45. B 4 2 3 1 9 8 7 6 5 C A E D State another name for 2

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