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# Part 8

 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.