1.
Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measures of two arcs. That is, if Q is a point on arc PR, then m(arc)PQ + m(arc)QR = m(arc) PQR
2.
Area Probability Postulate: If a point in region A is chosen at random, then the probability that the point is in region B, which is in the interior of region A, is area of region B over area of region A
3.
Circumference Of A Circle: If a circle has a circumference of C units and a radius of r units, then C=2(pi)r
4.
Definition Of Arc Measure: The measure of a minor arc is the measure of its central angle. The measure of a major arc is 360 minus the measure of its central angle. The measure of a semicircle is 180
5.
Exterior Angle Sum Theorem: If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360
6.
Interior Angle Sum Theorem: If a convex polygon has n sides and S is the sum of the measures of its interior angles, then S=180(n-2)
7.
Length Probability Postulate: If a point on line segment AB is chosen at random and C is between A and B, then the probability that the point is on line segment AC is length of line set AC over length of line set AB
8.
Postulate 10-1: The area of a region is the sum of the areas of all of its non overlapping parts
9.
Postulate 10-2: Congruent figures have equal areas
10.
Standard Equation Of A Circle: In general, an equation for a circle with center at (h, k) and a radius of r units is (x-h)squared + (y-k) squared = r squared
11.
Sum Of Central Angles: The sum of the measures of the central angles of a circle with no interior points in common is 360
12.
Theorem 9-1: In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent
13.
Theorem 9-2: In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc
14.
Theorem 9-3: In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center
15.
Theorem 9-4: If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc
16.
Theorem 9-5: If two inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc then the angles are congruent
17.
Theorem 9-6: If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle
18.
Theorem 9-7: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary
19.
Theorem 9-8: If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency
20.
Theorem 9-9: 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
21.
Theorem 9-10: If two segments from the same exterior point are tangent to a circle, then they are congruent
22.
Theorem 9-11: 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
23.
Theorem 9-12: 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
24.
Theorem 9-13: 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
25.
Theorem 9-14: If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal
26.
Theorem 9-15: 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
27.
Theorem 9-16: 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
28.
Theorem 11-1: If two solids are similar with a scale factor of a:b, then the surface areas have a ration of a squared: b squared and the volumes have a ratio of a cubed: b cubed
