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Warm – Up: Review of arc measures

Warm – Up: Review of arc measures. Warm – Up. Find each measure if AC and BD are diameters. m DEC mAB 3. mAD 4. mADC. A. B. E. D. 30 °. C. Properties of Chords. By the end of class today you will be able to:

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Warm – Up: Review of arc measures

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  1. Warm – Up: Review of arc measures

  2. Warm – Up Find each measure if AC and BD are diameters. • mDEC • mAB • 3. mAD • 4. mADC A B E D 30° C

  3. Properties of Chords • By the end of class today you will be able to: • Identify congruent minor arcs in the same circle or congruent circles using chords • Determine if a chord is a diameter • Determine if two chords are equal

  4. How do we know if two minor arcs are congruent?....

  5. Use congruent chords to find arc measures B • In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. C A D AB  CD IF AB  CD

  6. Examples

  7. Now You Try!

  8. Inscribed Polygons The square is inscribed in the circle. The square is inside the circle. Every vertex of the polygon touches the circle. The triangle circumscribes the circle. Sides touch. (All the way around. Like to circumnavigate the world means to go completely around the world.)

  9. JK  KL  JL Use congruent chords to find arc measures K Given JKL is equilateral, identify all congruent minor arcs. L J

  10. How do we know if a chord is a diameter?....

  11. If a chord is a perpendicular bisector of another chord, the first chord is a diameter.

  12. If a diameter is perpendicular to another chord, then the diameter bisects the chord and its arc.

  13. If a diameter is a perpendicular bisector of another chord, then it bisects both the chord and that chord’s arc.

  14. How do we know if two chords in a circle are congruent?....

  15. Congruent Chords Two chords are congruent if and only if they are equidistant from the center. B A M P AD  BC IF LP  PM L C D

  16. Congruent Chords IN A, PR = 2x + 5 and QR = 3x –27. Find x. R x x A P Q

  17. IMPORTANT!!! • With all things geometry, be sure to draw and LABEL everything! • So…If you know it is congruent, label it so!

  18. Practice Assignment: • Pg 201; 2-12 even • Pg 203; 2-12 even

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