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Volume of a triangular prism Bh Lateral Area of a triangular prism hp Surface area of a triangular prism LA+2B Volume of a sphere 4/3(pi)r^2 Surface area of a sphere 4(pi)r^2 Arc length x/360(2[pi]r) Central angle of a regular polygon 360/n Area of a sector x/360(pi)(r^2) Conditional statement if p, then q Converse if q, then p Inverse if not p, then not q Contrapositive if not q, then not p ratio for scale factors and for perimeters a/b ratio of areas (a/b)^2 The SUM of the measures of the INTERIOR angles of a CONVEX n-gon (n-2)(180) The measure of EACH INTERIOR angle of a REGULAR n-gon [(n-2)(180)]/n An angle whose vertex is on a circle and whose sides contain chords of the circle Inscribed Angle In the same circle (or in congruent circles), two chords are congruent if and only if... They are equidistant from the center Pythagorean Theorem (In a right triangle) a^2+b^2=c^2 Hypotenuse of a 30,60,90 triangle shorter leg x 2 Longer leg of 30,60,90 traingle shorter leg x square root of 3 Shorter leg of a 30,60,90 triangle hypotenuse/2 Hypotenuse of a 45,45,90 triangle leg x square root of 2 Perimeter Distance around the outside (add all sides) Circumference of a circle 2(pi)(r) or pi X d Skew lines lines that don't intersect and aren't coplanar Standard equation of a circle (x-h)^2 + (y-k)^2 = r^2 If one chord is a perpendicular bisector of another chord, then.... the first chord is a diameter Volume of a cylinder (pi)(r^2)(h) Surface area of a cylinder [2(pi)(r)(h)] + [2(pi)(r^2)] Pythagorean triple examples 3,4,5; 5,12,13; 8,15,17 Slope formula rise/run: (y1-y2)/(x1-x2) Slopes of parallel lines are.... equal Perpendicular lines have______ slopes negative reciprocal A segment with endpoints on the circle chord If an angle is inscribed in a circle, then its measure is.... 1/2 the measure of its intercepted arc A line that intersects a circle in two points secant Lateral area of a cylinder 2(pi)(r)(h) The AREA of a REGULAR n-gon (1/2)(a)(p) The measure of EACH EXTERIOR angle of a REGULAR n-gon 360/n If two segments from the same exterior point are tangent to a circle, then..... they are congruent In the same circle (or in cngruent circles), two minor arcs are congruent if and only if.... their corresponding chords are congruent If a diameter of a circle is perpendicular to a chord, then...... the diameter bisects the chord and its arc If two inscribed angles of a circle intercept the same arc, then.... the angles are congruent A quadrilateral 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 on a circle, then.... the measure of each angle formed is 1/2 the measure of its intercepted arc Volume of a square pyramid (1/3)Bh Lateral area of a square pyramid (1/2)(L)(p) Surface area of a square pyramid LA + B Area of a triangle (1/2)bh Area of a parallelogram bh Area of a rectangle bh; lw Area of a square bh; s^2 Area of a trapeziod (1/2)(h)(b1 + b2) Area of a circle (pi)(r^2) If a line is tangent to a circle, then its perpendicular to.... the radius that drawn to the point of tangency A line or segment that is tangent to two coplanar circle common tangent Coplanar circles that intersect in one point Tangent circles Volume of a rectangular solid lwh SIN (only in a RIGHT triangle) opposite/hypotenuse COS (only in a RIGHT triangle) adjacent/hypotenuse TAN (only in a RIGHT triangle) opposite/ adjacent Distance Formula square root of: [(x1-x2)^2 + (y1 - y2)^2] Midpoint formula (avg. X, avg. Y): { [(x1+x2)/2], [(y1+y2)/2] } Coplanar circles that have a common center Concentric circles Dodecahedron 12 faces Icosahedron 20 faces Algebra rule to rotate 90degrees (x,y) ---> (-y,x) Algebra rule to rotate 180degrees (x,y) ---> (-x,-y) Algebra rule to rotate 270degrees (x,y) ---> (y, -x) Algebra rule to reflect over x-axis (x,y) ---> (x,-y) Algebra rule to reflect over y-axis (x,y) ---> (-x,y) Algebra rule to reflect over y=x (x,y) ---> (y,x) Algebra rule to reflect over y=-x (x,y) ---> (-y,-x) Maximum area formula (p/4)^2 Measure of an angle with a vertex in the center of a circle measure of its arc Measure of an angle with a vertex on the circle 1/2 measure of its arc Measure of an angle with a vertex inside the circle 1/2 (sum of the arcs) Measure of an angle with a vertex outside the circle 1/2 (difference of the arcs)