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Angles in Circles

Angles in Circles. CENTRAL & INSCRIBED ANGLES. OBJECTIVES. Understand the meaning of: Central angles Inscribed angles Be able to solve problems involving angles in circles. ANGLES IN CIRCLES. A central angle is . . .

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Angles in Circles

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  1. Angles in Circles CENTRAL & INSCRIBED ANGLES

  2. OBJECTIVES • Understand the meaning of: • Central angles • Inscribed angles • Be able to solve problems involving angles in circles

  3. ANGLES IN CIRCLES A central angle is . . . AN ANGLE WITH ITS VERTEX AT THE CENTER OF A CIRCLE AND SIDES PASSING THROUGH THE ENDPOINTS OF AN ARC. THE SIDES OF THE ANGLES ARE RADII.

  4. ANGLES IN CIRCLES CENTRAL ANGLE

  5. ANGLES IN CIRCLES The measure of an arc is the same as the measure of its CENTRAL ANGLE. D O G

  6. INSCRIBED ANGLES An inscribed angle has its vertex on the circle, and its sides are chords. C T A

  7. DON’T MIX CATS & DOGS!! CAN YOU TELL THE DIFFERENCE BETWEEN A CENTRAL ANGLES & AN INSCRIBED ANGLE??

  8. DON’T MIX CATS & DOGS!! CAN YOU TELL THE DIFFERENCE BETWEEN A CENTRAL ANGLES & AN INSCRIBED ANGLE??

  9. WHAT’S THE MEASUREOF AN INSCRIBED ANGLE? 500 ??0 500

  10. INSCRIBED ANGLE THEOREM The measure of an inscribed angle is equal to one-half ( ) the measure of its intercepted arc, or the measure of the central angle which intercepts the arc.

  11. INSCRIBED ANGLES INTERCEPTING ARCS THEOREM Inscribed angles that intercept the same arc arecongruent.

  12. ANGLES INSCRIBED IN A SEMICIRCLE 900 1800

  13. ANGLES INSCRIBED IN A SEMIRCLE THEOREM Angles inscribed in a semicircle are RIGHT ANGLES

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