1. Name a plane. 2. Name a line. 3. Name a ray. 4. Name a point. 5. Name three collinear points. 6. Name four coplanar points. 7. Name a segment. 8. Do points T and Q lie on the same line? 9. Plane RYT  plane EWTR is _______. 10. How many planes does point S lie on?

Homework Answers pg. 15 5)True 6)False 7)True 8)True 9)False 10) True 11) False 12) True 13) True 14) False 15) True 16) False 17) False 18) True pg ) x = 6 34) x = 11 35) x = 3 36) x = 7 37) y = 6 38) y = 7 39) z = 8 GE = 10, EH = 10 E is the midpoint of GH 40) z = 5 GE = 5, EH = 6 E is not the midpoint of GH

In this section we will discuss the proper notation of angles, specific classifications of angles, and the properties of angle bisectors and the Angle Addition Postulate.

C A T Angle – the figure formed by two rays that have the same endpoint. The two rays are called the sides; the shared endpoint is called the vertex. Vertex Sides

We name an angle using three letters and the  symbol. Order Matters!! The vertex must be the letter in the middle! C AT Acceptable:  CAT  TAC Unacceptable:  ACT  TCA

Alternative Notation C TA You can name an angle just with the vertex. This angle could be  A. Sometimes using only one letter may not be specific enough, because it may refer to more than one angle. IF THERE IS ANY DOUBT, USE THREE LETTERS! B  CAB  CAT  BAT

We also may name angles with numbers. C T B A 1 2  CAB is  1  BAT is  2

Measuring Angles We measure angles using a protractor. The units for angle measurement is degrees. Symbol for Degree: Measure of Angle: m  ABC 70°

Measure Angles #1-9 using your protractor. Estimate to the nearest degree.

Classifying Angles Acute Angle Obtuse Angle Right AngleStraight Angle A pair of opposite rays creates a straight angle. An angle measuring between 0  and 90 . An angle measuring between 90  and 180 . An angle measuring exactly 90  An angle measuring exactly 180 

Angle Interior Any points that lie inside the angle. A B C D T E H

Congruent Angles Recall the Definition of Congruent: Figures that are the same shape and size. Congruent Angles – angles that have equal measures.  MAT   ZIPm  MAT  m  ZIP Remember: Figures can be congruent; measures can be equal. M A T Z I P 120°

Adjacent Angles Definition: two angles in a plane that have a common vertex and a common side but no common interior points. C T B A  CAB and  BAT are adjacent angles.  CAT and  BAT are NOT adjacent because they share interior points.

Angle Bisector Definition: a ray that divides an angle into two congruent adjacent angles. 60  X Y Z W is an angle bisector.  XWY  YWZ

Angle Addition Postulate 50  65  A B C O If B lies on the interior of  AOC, then m  AOB + m  BOC = m  AOC. m  AOC = 115 

B Q D C m  BQC = x - 7m  CQD = 2x - 1 m  BQD = 2x + 34 Find x, m  BQC, m  CQD, m  BQD. m  BQC + m  CQD = m  BQD 3x – 8 = 2x + 34 x – 7 + 2x – 1 = 2x + 34 x – 8 = 34 x = 42 m  BQC = 35 m  CQD = 83 m  BQD = 118

Update Postulate Section – Angle Addition Postulate