## FLVS Geometry Segment 2 Module 7 Theorems, Postulates, and Vocab

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JCDenbaugh  on August 7, 2012

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# FLVS Geometry Segment 2 Module 7 Theorems, Postulates, and Vocab

 7-1 Arc Additions PostulateThe measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs.
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#### Definitions

7-1 Arc Additions Postulate The measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs.
7-1 Congruent Arcs Theorem In the came circle of in two congruent sides, two arcs are congruent if and only if their corresponding central angles are congruent.
7-2 Congruent Arcs and Chords Theorem In a circle or congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
7-2 Congruent Chords, Congruent Central Angles Postulate If two chords are of equal length, then the central angles are equal.
7-3 Perpendicular Diameters and Chords Theorem In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.
7-4 Equidistant Chords are Congruent Theorem In a circle or in congruent circles, if two chords are equidistant from the center of the circle, they are congruent.
7-5 Inscribed Angle Theorem The measure of an inscribed angle is one-half the measure of its intercepted arc.
7-6 Inscribed Angles and Congruent Arcs Theorem If two inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent.
7- 7 Inscribed Angles and Semicircles Theorem If an inscribed angle intercepts a semicircle, then the angle is a right angle.
7- 8 Inscribed Quadrilaterals in Circles Theorem If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Theorem 7-9 If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Theorem 7-10 If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of its intercepted arc.
Theorem 7-11 If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
Theorem 7-12 If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
Theorem 7-13 If a line is perpendicular to a radius of a circle at its endpoint on the circle, then it is a tangent.
Theorem 7-14 If two segments from the same exterior point are tangent to a circle, then they are congruent.
7-15 Two Intersecting Chords Theorem If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal.
7-16 Two Secants from the Same Point Theorem If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
7-17 A Secant and a Tangent from the Same Point Theorem If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Circle the set of all point equidistant from a given point, called the center
Radius the distance from the center to the circle itself
Congruent Circles if the radii of two or more circles are congruent
Chord a line segment whose endpoints are on the circle
Diameter a chord that passes through the center
Concentric Circles circles that lie in the same plane and have the same center
Circumference the distance around the outside of the circle
Tangent a line that intersects the circle in exactly one point
Point of Tangency the point of intersection of the tangent and the circle
Secant a line that intersects the circle at exactly 2 points
Inscribed Polygon a polygon is drawn inside a circle so that its vertices are on the circle
Circumscribed Circle the circle around the polygon
Inscribed Circle the circle inside the polygon
Circumscribed Polygon a polygon that has all of its sides tangent to a circle
Central Angle an angle whose vertex is the center of the circle.
Arc an unbroken part of a circle
Minor Arcs less than 180 degrees and are represented by two letters.
Major Arcs more than 180 degrees and are represented by three letters.
Semi-Circles formed by the diameter of a circle separating the circle into two arcs.
Adjacent arcs arcs of a circle that have exactly one point in common
Sector the region between two radii of a circle and the included arc
Segment of a Circle the region between a chord of a circle and the included arc
Annulus the area between two concentric circles
Geometric Probability the ratio of the area of a specific region in a figure compared to the area of the entire figure
Inscribed Angle an angle whose vertex is on the circle itself
Intercepted Arcs arcs created by inscribed angles

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