Theorems Related to circle and its parts.pptx

This power point presentation is about the theorems related to the parts of circle

1. THEOREMS ON CIRCLE

2. ARCS Arc is a part of a circumference of a circle. It is named by their endpoints and can be read clockwise or counter-clockwise. The symbol for arc is

3. CHORD A chord is a segment which endpoints are on a given circle.

4. INSCRIBED ANGLE Inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.

5. INSCRIBED ANGLE B D E C

6. INTERCEPTED ARC Intercepted arc is the arc that lies in the interior of an angle and has endpoints on the angle.

7. INTERCEPTED ARC B D A C E

8. In the same circle or in congruent circles: a. Congruent arcs have congruent chords. b. Congruent chords have congruent arcs Chord arcs theorem B D A C E

9. If a diameter or a radius is perpendicular to a chord, and then it bisects the chord and its arc with the same endpoints. Perpendicular bisector theorem S R T Y A X

10. The measure of the inscribed angle is equal to one-half of its intercepted arc (or the measure of the intercepted arc is twice the measure of the inscribed angle). INSCRIBED ANGLE theorem A R T S

11. If two inscribed angles of a circle intercept the same arc, then the angles are congruent. CONGRUENT INSCRIBED ANGLE theorem A R S T Y

12. If an inscribed angle intercepts a diameter or semicircle, then the angle is a right angle. THALE’S theorem A R S T

13. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. CYCLIC QUADRILATERAL theorem H M S I T