|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.|
Note: The concepts in this collection may
not be entirely accurate.
They are for reference only.