4th Quarter Math Notes

**Cassandra** Thu Jan 21, 2010 10:43 pm

Math Theorems

Theorem # 1:
In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Theorem # 2:
In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.

Theorem # 3:
In a circle, two chords are congruent if and only if they are equidistant from the center.

Theorem # 4:
If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc.

Theorem # 5:
If two inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent.

Theorem # 6:
If an inscribed angle of a circle intercepts a semicircle, then the angles is a right angle.

Theorem # 7:
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

Theorem # 8:
In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is a tangent of the circle.

Theorem # 9:
If two segments from the same exterior point are tangent to a circle, then they are congruent.

Theorem # 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 # 11:
If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Theorem # 12:
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 arc.

**Cassandra** Wed Jan 27, 2010 9:15 pm

Definition of Terms

circle
a set of points that consists of all points in a plane that are a given distance from a given point in the plane, called the center
diameter
a chord that contains the center of a circle
radius
a segment whose endpoints are the center of the circle and a point on the circle
chord
a segment whose endpoints are points on the circle
center of a circle
a point from which all given points in a plane are equidistant
inscribed angle
an angle having its vertex lie on a given circle and containing two chords of the circle
central angle
an angle that intersects the circle in two points and has its vertex at the center of the circle
arc
an unbroken part of a circle
tangent
a line in the plane of a circle that intersects the circle in exactly one point; the point of intersection is called the point of tangency
secant
a line that intersects the circle in exactly two points
circumference of the circle
limit of the perimeters of the inscribed regular polygons as the number of sides increases
intercepted arc
an angle intercepts an arc if and only if each of the following conditions hold:
- endpoints of the arc lie on the angle
- all endpoints of the arc, except the endpoints, are in the interior of the circle
- each side of the angle contains an endpoint of an arc