Definitions, Postulates, Theorems for chapters 8-14 for Geometry
chapter 8 through 14 theorems, postulates, definitions and corollaries
Terms
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- the measure of a major arc is 360 minus the measure of its minor arc
- measure of a major arc
- Theorem 9-3
- in the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent
- arcs that have exactly one point in common
- adjacent arcs
- the interior of the central angle
- minor arc
- Theorem 9-4
- in the same circle or in congruent circles: congruent arcs have congruent chords
- the exterior of the central angle
- major arc
- an angle with its vertex at the center of the circle
- central angle
- Theorem 9-6
- In the same circle or in congruent circles: chords equally distant from the center (or centers) are congruent
- Theorem 9-6
- In the same circle or in congruent circles: chords are equally distant from the center (or centers)
- circles/spheres that have congruent radii
- congruent circles/spheres
- set of points in a plane at a given distance from a given point in that plane
- circle
- spheres that have the same center
- concentric spheres
- the measure of a minor arc is defined to be the measure of its central angle
- measure of a minor arc
- segment whose endpoints lie on a circle
- chord
- Corollary 9-1
- tangents to a circle from a point are congruent
- the measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs
- arc addition postulate
- 180
- measure of a semicircle
- Theorem 9-4
- in the same circle or in congruent circles: congruent chords have congruent arcs
- line in the plane of a circle that intersects the circle in exactly one point
- tangent
- line that contains a chord
- secant
- tangent that intersects the segment joining the centers
- common internal tangent
- the given point of the circle
- center
- the point in which a tangent intersects a circle
- point of tangency
- chord that contains the center of a circle
- diameter
- theorem 9-2
- if a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle
- the given distance
- radius
- theorem 9-1
- if a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency
- line that is tangent to each of two coplaner circles
- common tangent
- coplaner circles that are tangent to the same line at the same point
- tangent circles
- Theorem 9-5
- a diameter that is perpendicular to a chord bisects the cord and its arc
- tangent that does not intersect the segment joining the centers
- common external tangent
- circles that lie in the same plane and have the same center
- concentric circles