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Section 1-4

Section 1-4. Angles. Angle – figure formed by 2 rays that have the same endpoint. The rays are the _______. The common endpoint is the _________. When naming an angle, use __ letters, __ letter, or ___ number. Vertex = ______ Name the angle. Sides = ____ and ____. sides. vertex.

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Section 1-4

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  1. Section 1-4 Angles

  2. Angle – figure formed by 2 rays that have the same endpoint. The rays are the _______. The common endpoint is the _________. When naming an angle, use __ letters, __ letter, or ___ number. Vertex = ______ Name the angle. Sides = ____ and ____ sides vertex 3 1 1 point B ABC, CBA, 4, B

  3. DBC, ABC ABD, Name 3 angles.

  4. degrees right acute Angles are measured in _________. There are 4 classifications of angles. _______________ _______________ Measures between Measure _______ _____ and _____ ________________ _______________ Measures between Measure _______ ______ and _______ 90° 90° 0° obtuse straight 180° 90° 180°

  5. Protractor Postulate: Given QOP, if is paired with x and is paired with y, then mQOP = . Example 1 20° and 90° Example 2 90° and 120° Example 3 90° and 40° = 70° = 30° = 50°

  6. Angle Addition Postulate: If point B lies in the interior of AOC, then mAOB + mBOC = mAOC. Angle Addition Postulate: If AOC is a straight angle, then mAOB + mBOC = 180°.

  7. Find x, mABC, mCBD. mABC = (7x)° mABC = 7(20) mABC = 140° mCBD = (2x)° Angle Addition Postulate mCBD = 2(20) mABC + mCBD = mABD mCBD = 40° 7x + 2x = 180 9x = 180 x = 20

  8. Find x and the other angle measures. (3x + 4)° 3(18) + 4 58° Angle Addition Postulate (2x – 4)° 2(18) – 4 (3x + 4) + (2x – 4) = 90 3x + 4 + 2x – 4 = 90 32° 5x = 90 x = 18

  9. equal measures congruent angles – angles that have ____________ _______________ adjacent angles – 2 angles in a _______ that have a _________ ________ and a _________ ______, but no common interior points plane common common vertex side nonadjacent adjacent nonadjacent adjacent nonadjacent

  10. ray congruent bisector of an angle – a ______ that divides an angle into 2 _____________ angles Ex. Given: bisects BED, mAEB = (19x)°, mBEC = (8x + 20)° Find x and mCED. (19x) + (8x + 20) + (8x + 20) = 180 19x + 8x + 20 + 8x + 20 = 180 35x + 40 = 180 35x = 140 (8x + 20)° x = 4 (8x + 20)° (19x)° mCED = (8x + 20)° mCED = 8(4) + 20 mCED = 52°

  11. Examples: Give another name for each angle. 1. DEB 2. CBE 3. BEA 4. DAB 5. 7 6. 9 8 3 1 C, ABE DCB, ECB, DCA, ECA

  12. EAB AEC 7. m1 + m2 = m______ 8. m3 + m4 = m______ 9. m5 + m6 = m______ or ______ EDC 180°

  13. point B 8 or BED 10. Name the vertex of 3. 11. Name the right angle.

  14. A or BAE State another name for each angle. 12. 1 13. 6 14. EBD 15. 4 BDC 3 DBC

  15. 7 ABE 16. BDE or BDA 17. 2 18. 5 19. 9 C or BCD BEA

  16. HOMEWORK: page 21 #2-34 even

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