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Geometry: Tools of Geometry

Geometry: Tools of Geometry. Angle Relationships. Do Now:. m<1= 5x+1 m<2 = 2x - 12 m<3= 6x-5 m<ABC= 127 Find x. Homework. Struggles? Concerns? Confusions? Ask away!!!. Comment. Grades This week/Next Week. Angle Relationships. Review: Congruent Angles Right Angles

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Geometry: Tools of Geometry

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  1. Geometry: Tools of Geometry Angle Relationships

  2. Do Now: m<1= 5x+1 m<2 = 2x-12 m<3= 6x-5 m<ABC= 127 Find x

  3. Homework • Struggles? • Concerns? • Confusions? • Ask away!!!

  4. Comment • Grades • This week/Next Week

  5. Angle Relationships • Review: • Congruent Angles • Right Angles • Straight Angles • Opposite Rays

  6. Note • An angle divides a plane into three distinct parts. • Points that lie • Points that lie • Points that lie

  7. Note • An angle divides a plane into three distinct parts. • Points that lie on the angle • Points that lie in the interior of the angle • Points that lie in the exterior of the angle

  8. Adjacent Angles • Two angles that lie in the same plane and have a common vertex and a common side, but no common interior points.

  9. Vertical Angles • Two nonadjacent angles formed by two intersecting lines.

  10. Note • Vertical angles are always congruent

  11. Complementary Angles • Two angles whose measure sums to 90 degrees.

  12. Supplementary Angle • Two angles whose measures sums to 180 degrees.

  13. Example One: True/False? <BFD and <CFD are adjacent angles <AFB and <EFD are vertical angles <AFE and <BFC are complementary angles

  14. Linear Pair • Pair of adjacent angles with non-common sides that are opposite rays (i.e. a straight angle. i.e. a line)

  15. Example Two: • ∠KPL and ∠JPL are a linear pair, m∠KPL=2x+24, and m∠JPL=4x+36. What are the measures of ∠KPL and ∠JPL?

  16. Perpendicular • Lines, segments or rays that form right angles are perpendicular.

  17. Angle Bisector • A ray, segment, or line that bisects an angle, splits that particular angle into TWO EQUAL pieces.

  18. Example Three: • AC bisects m∠DAB. If ∠DAC=58, what is m∠DAB?

  19. Example Four:

  20. Practice • Practice some on your own/in small groups! • Call me over if you are confused!

  21. Exit Ticket • Ray BS bisects <ABC . If m<ABC = 104, what is m<SBC?

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