10.1 Angles in Circles
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10.1 Angles in Circles

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10.1 Angles in Circles 10.1 Angles in Circles Document Transcript

  • 10.1 Angles in Circles 1 March 24, 2014 Circle Geometry 10.1 Exploring Angles in a Circle
  • 10.1 Angles in Circles 2 March 24, 2014 Anatomy of a Circle What do we know about a circle?
  • 10.1 Angles in Circles 3 March 24, 2014 Anatomy of a Circle Chord: A line segment with both endpoints on a circle
  • 10.1 Angles in Circles 4 March 24, 2014 Anatomy of a Circle Central Angle: An angle formed by two radii of a circle.
  • 10.1 Angles in Circles 5 March 24, 2014 Anatomy of a Circle Inscribed Angle: An angle formed by two chords that share a common endpoint
  • 10.1 Angles in Circles 6 March 24, 2014 Anatomy of a Circle Arc (of a circle): A portion of the circumference
  • 10.1 Angles in Circles 7 March 24, 2014 Properties of Angles The inscribed angles subtended by the same arc are congruent.
  • 10.1 Angles in Circles 8 March 24, 2014 Tips and Tricks If you see a bow tie, you have sets of inscribed angles.
  • 10.1 Angles in Circles 9 March 24, 2014 Properties of Angles The measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc. B A C O
  • 10.1 Angles in Circles 10 March 24, 2014 Tips and Tricks If you see a Star Trek insignia, you have a set of inscribed angles and central angles.
  • 10.1 Angles in Circles 11 March 24, 2014 Example Find ∠ACD and ∠AOD if ∠ABD is 35˚
  • 10.1 Angles in Circles 12 March 24, 2014 Example Find ∠ACD and ∠AOD if ∠ABD is 35˚
  • 10.1 Angles in Circles 13 March 24, 2014 Properties of Angles Angles inscribed in a semicircle are right angles.
  • 10.1 Angles in Circles 14 March 24, 2014 Example Point C is the centre of the circle. The diameter AB is 10cm and the chord BD is 6 cm. B D C A
  • 10.1 Angles in Circles 15 March 24, 2014 Example Determine the measure of the missing angle
  • 10.1 Angles in Circles 16 March 24, 2014 Example Determine the measure of angle y
  • 10.1 Angles in Circles 17 March 24, 2014
  • 10.1 Angles in Circles 18 March 24, 2014 Example Determine the measure of the missing angles
  • 10.1 Angles in Circles 19 March 24, 2014 Example Determine the measure of the missing angles
  • 10.1 Angles in Circles 20 March 24, 2014 Example Determine the measure of the missing angle
  • 10.1 Angles in Circles 21 March 24, 2014 Questions page 382 3, 4, 10, 12, 20a