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©1998 ThinkQuest
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©1998 ThinkQuest
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| Theorem 10.7 | If two non-vertical lines are parallel, then they have equal slopes. |
| Theorem 10.8 | If the product of the slopes of two non-vertical perpendicular lines is -1, then the lines are perpendicular. |
| Theorem 10.9 | The product of the slopes of two non-vertical perpendicular lines is - 1. |
| Theorem 11.1 | If a line or segment contains the center of a circle and is perpen- dicular to a chord, then it bisects the chord. |
| Theorem 11.2 | In the same circle or in congruent circles, congruent chords are equidistant from the center(s). |
| Theorem 11.3 | In the same circle or in congruent circles, chords that are equidistant from the center(s) are congruent |
| Theorem 11.4 | In the same circle or congruent circles, if two chords are unequally distant from the center(s), then the chord nearer its corresponding center is the longer chord. |
| Theorem 11.5 | In the same circle or congruent circles, if two chords are unequal in length, then the longer chord is nearer the center of its circle. |
| Theorem 11.6 | If a line is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. |
| Theorem 11.7 | If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. |
| Theorem 11.8 | Two segments drawn tangent to a circle from an exterior point are congruent. |
| Corollary | The angle between two tangents to a circle from an exterior point is bisected by the segment joining its vertex and the center of the circle. |
| Postulate 19 | If P is a point on A-PB, then mA_B + mFB_ = mX-P-B. |
| Theorem 11.9 | In the same circle or in congruent circles: 1. If chords are congruent, then their corresponding arcs and central angles are congruent; 2. If arcs are congruent, then their corresponding chords and central angles are congruent; 3. If central angles are congruent, then their corresponding arcs and chords are congruent. |
| Theorem 11.10 | Inscribed Angle Theorem: The measure of an inscribed angle is one-half of the degree measure of its intercepted arc. |
| Corollary 1 | If two inscribed angles intercept the same arc or congruent arcs, then the angles are congruent. |
| Corollary 2 | An angle inscribed in a semicircle is a right angle. |
| Corollary 3 | If two arcs of a circle are included between parallel chords or secants, then the arcs are congruent. |
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Note: The concepts in this collection may
not be entirely accurate.
They are for reference only.
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