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Chords, Secants, & Tangents ( Angle Measures )

Chords, Secants, & Tangents ( Angle Measures ). 9.3.3.8 Know and apply properties of a circle to solve problems and logically justify results. . Guiding Question: How do I measure intersecting lines in & out of a circle?.

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Chords, Secants, & Tangents ( Angle Measures )

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  1. Chords, Secants, & Tangents (Angle Measures) 9.3.3.8 Know and apply properties of a circle to solve problems and logically justify results.

  2. Guiding Question: How do I measure intersecting lines in & out of a circle? • Lesson Obj: IWBAT know the properties of a circle and solve problems using them. • Vocabulary • Chords • Secants • Tangents • Major/Minor Arc

  3. Guiding Question: How do I measure intersecting lines in & out of a circle? Chords: Any segment with 2 endpts on the circle. Secant: A line passing through a circle Tangent: A line crossing a circle at 1 pt. called a pt. of tangency.

  4. Guiding Question: How do I measure intersecting lines in & out of a circle? Recall that a central angle measure is congruent to its arc. An inscribed angle is made by 2 chords with a same endpoint.

  5. Guiding Question: How do I measure intersecting lines in & out of a circle? • What is the angle measure of x? • How big is the intercepted arc?

  6. Guiding Question: How do I measure intersecting lines in & out of a circle? If 2 (or more) inscribed angles intercept the same arc, they are congruent! What if I have intersecting chords? How could I find the measure of angles 1 and 2? What kind of angles are they?

  7. Guiding Question: How do I measure intersecting lines in & out of a circle? • 2 chords intersect: Average the measure of the intercepted arcs.

  8. Guiding Question: How do I measure intersecting lines in & out of a circle? • For any angle outside the circle(2 secants, 1 secant & 1 tangent): Big arc – small arc and divide it by 2.

  9. Guiding Question: How do I measure intersecting lines in & out of a circle? For this it will be half of 170 What is the measure of k?

  10. Guiding Question: How do I measure intersecting lines in & out of a circle? • Summary: • Inscribed Angles: Half of central angle intercepting same arc • Intersecting chords: Add up the intercepted arcs and divide by 2 • 2 secants: Big arc – little arc, then divide by 2 • 1 tangent & 1 secant/chord – half of intercepted arc.

  11. Guiding Question: How do I measure intersecting lines in & out of a circle? • Assignment: Worksheet

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