WARMUP I. Solve the following 1.Plane GEDF and plane DFBC intersect at? 2.Plane EADB and plane EGAH intersect at? 3.Line EG and line DE intersect at? 4.

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Presentation transcript:

WARMUP I. Solve the following 1.Plane GEDF and plane DFBC intersect at? 2.Plane EADB and plane EGAH intersect at? 3.Line EG and line DE intersect at? 4. Line AH and line HC intersect at? 5. Name 2 planes that do not intersect 6. Name 2 lines that do not intersect. 7. Say ED is a segment and imagine point Q is the midpoint of segment ED. If segment EQ = 3x – 5 and segment QD = 2x + 6, solve for x, EQ, QD, and ED.

ANGLES AND ANGLE ADDITION AGENDA: WARMUP ANGLES NOTES/PRACTICE QUIZ MONDAY UNIT 2 TEST FRIDAY

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 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 either degrees or radians. In this class we will use degrees. Symbol for Degree: 45  Measure of Angle: m  ABC

Classifying Angles Acute Angle Obtuse Angle Right AngleStraight Angle Note: “between” means we do not include the endpoints. An angle measuring between 0  and 90 . An angle measuring between 90  and 180 . An angle measuring exactly 90  An angle measuring exactly 180 

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° Remember: rays go off in one direction forever!

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

Example 2: Find m  DBCExample 3: Find m  QST ABC D 38° m  ABC = 180 m  DBC = 180 – 38 m  DBC = ° m  RST = 128 m  RST = 128 – 91 m  RST = 37 R Q T S 91° 37°

Check for Understanding  P. 38 #15-29  P. 65 #17-22  P. 66 #28-30

Algebra Connection 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 m  BQC = x – 7 m  CQD = 2x – 1 x = 42 m  BQC = 42 – 7 = 35 m  CQD = 2(42) – 1 = 83 m  BQD = 2x + 34 m  BQD = 2(42) + 34 = 118 CHECK: = 118