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©1998 ThinkQuest
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©1998 ThinkQuest
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| Corollary 4 | The opposite angles of an inscribed quadrilateral are supplementary. |
| Theorem 11.11 | The measure of an angle formed by two secants or chords intersecting in the interior of a circle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. |
| Theorem 11.12 | The measure of an angle formed by two secants intersecting in the exterior of the circle is one-half the difference of the measures of the intercepted arcs. |
| Theorem 11.13 | If a tangent and a secant (or a chord) intersect at the point of tangency on a circle, then the measure of the angle formed is one-half the measure of its intercepted arc. |
| Theorem 11.14 | The measure of an angle formed either by (1) a tangent and secant intersecting at a point exterior to a circle, or (2) two tangents intersecting at a point exterior to a circle equals one-half the difference of the measures of the intercepted arcs. |
| Theorem 11.15 | If two chords of a circle intersect, then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord. |
| Theorem 11.16 | If a tangent and a secant intersect in the exterior of a circle, then the square of the length of the tangent segment equals the product of the lengths of the secant segment and the external secant segment. |
| Corollary | If two secants intersect in the exterior of a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. |
| Theorem 11.17 | The equation of a circle with the coordinates of the center (b,k) and a radius of length r is (x - h)' + (y - k)l = r. |
| Postulate 20 | Congruent polygons have equal areas. |
| Postulate 21 | The area of a rectangle is the product of the lengths of a base and a corresponding altitude (Area of rectangle = bb). |
| Theorem 12.1 | The area of a square is the square of the length s of a side (A = S2). |
| Postulate 22 | Area Addition Postulate: If a region is the union of two or more nonoverlapping regions, then its area is the sum of the areas of these nonoverlapping regions. |
| Theorem 12.2 | The area of a parallelogram is the product of the lengths of a base and a corresponding altitude (Area of parallelogram = bb). |
| Theorem 12.3 | The area of a triangle is one-half the product of the lengths of a base and a corresponding altitude (Area of triangle = lbh). |
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Note: The concepts in this collection may
not be entirely accurate.
They are for reference only.
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