Arc Addition Postulate

The meausre of an arcformed by two adjacent arcs is the sum of the measures of the two arcs.

In a plane, a line is a tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.

Tangent segments from a common external point are congruent.

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

If one chord is a perpendicular bisector of another chord, then the first chord is a diamteter.

IF a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

In the same circle, or in congruent circlres, two chods are congruent if and only if they are equidistant from the center.

Measure of an Inscribed Angle Theorem

The measure of an inscribed angle is one half the measure of its intercepetd arc.

If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

If a right triangle is inscribed in circle then the hypotenuse is a diameter of the circle.Conversely if one side of a inscribed triangle is diameter of the circle then the triangle is right triangle and the angle opposite the diameter is the right angle.

A quadrilater can be inscribed in a circle if and only if its opposite angles are supplementary.

If a tangent and a chord intersect at a point ofn a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

Angles Inside the Circle

If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Angles Outside the Circle

If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arc.s

Segments of Chords Theorem

If two chrods intersect in the interior of a circle, then the porduct of the lenghts of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Segments of Secants Theorem

If two secant segments share the same ednpoint outiside a circle, then the porduct of the lenghts of one secant segmetn and its external segment equals the product of the lenghts of the other secant segments and its external segment.

Segments of Secants and Tangents Thoerem

If a secant segment and a taangent segment share an endpont outside a circle, then the porduct of the lenghs of the secant segment and its external segment equals the square of the lenght of the tangent segment.

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Ch10postthms

Chapter 10 Postulates and Theorems

Name	Definition
Arc Addition Postulate	The meausre of an arcformed by two adjacent arcs is the sum of the measures of the two arcs.
10.1	In a plane, a line is a tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.
10.2	Tangent segments from a common external point are congruent.
10.3	In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
10.4	If one chord is a perpendicular bisector of another chord, then the first chord is a diamteter.
10.5	IF a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
10.6	In the same circle, or in congruent circlres, two chods are congruent if and only if they are equidistant from the center.
Measure of an Inscribed Angle Theorem	The measure of an inscribed angle is one half the measure of its intercepetd arc.
10.8	If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
10.9	If a right triangle is inscribed in circle then the hypotenuse is a diameter of the circle.Conversely if one side of a inscribed triangle is diameter of the circle then the triangle is right triangle and the angle opposite the diameter is the right angle.
10.10	A quadrilater can be inscribed in a circle if and only if its opposite angles are supplementary.
10.11	If a tangent and a chord intersect at a point ofn a circle, then the measure of each angle formed is one half the measure of its intercepted arc.
Angles Inside the Circle	If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Angles Outside the Circle	If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arc.s
Segments of Chords Theorem	If two chrods intersect in the interior of a circle, then the porduct of the lenghts of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
Segments of Secants Theorem	If two secant segments share the same ednpoint outiside a circle, then the porduct of the lenghts of one secant segmetn and its external segment equals the product of the lenghts of the other secant segments and its external segment.
Segments of Secants and Tangents Thoerem	If a secant segment and a taangent segment share an endpont outside a circle, then the porduct of the lenghs of the secant segment and its external segment equals the square of the lenght of the tangent segment.

Created by: mstrmoe

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