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GEOMETRY VOLUME AND SURFACE AREA FORMULAS

STUDY
PLAY
Lateral area
Ph
Surface Area
L + 2B
Surface Area of Cylinder
2πrh + 2πr^2
Surface area of Pyramid
1/2Pl + B
Surface Area of Cone
πrl + πr^2
Surface Area of Sphere
4πr^2
Volume of a prism
Bh
Volume of a Cylinder
πr^2h
Volume of a Pyramid
(1/3)Bh
Volume of a Cone
(1/3)πr^2h
Volume of a Sphere
(4/3)πr^3
Area of a Sector
(N/360)πr^2
Third Angle Theorem
If 2 angles of one triangle are congruent to two angles of a second triangle, the third angles of the triangle are congruent.
Circumcenter Theorem
The circumcenter of a triangle is equidistant from the vertices
Incenter Theorem
THe incenter of a triangle is equidistant from each side of the triangle
Centroid Theorem
The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median
Circumcenter
Point of concurrency of perpendicular bisectors
Incenter
point of concurrency of angle bisectors
Centroid
Point of concurrency for the medians of a triangle
Orthocenter
intersection point of altitudes
Isosceles Triangle Theorem
If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent
SSS Similarity
if the measure of the corresponding sides of 2 triangles are proportional, then the triangles are similar
SAS Similarity
If the measure of 2 sides of a triangle are proportional to the measure of 2 corresponding sides of another triangle, and the included angles are congruent, then the triangles are similar
Triangle Proportionality Theorem
If a line is parallel to one side of a triangle and intersects the other 2 sides in 2 distinct points, then it separates these sides into segments of proportional lengths
Proportional Perimeters Theorem
If 2 triangles are similar, then the perimeters are proportional to measure of corresponding sides
Angle Bisector Theorem
An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other 2 sides
Law of Sines
(sin A)/a = (sin B)/b = (sin C)/c
Law of Cosines
a^2 = b^2 + c^2 - 2bc cos A
Parallelogram
Diagonals bisect, opposite sides congruent, consecutive angles supplementary, opposite angles congruent, one pair of opposite sides parallel and congruent
Rectangle
Same properties as parallelogram, diagonals are congruent
Rhombus
Diagonals are perpendicular, Each diagonal bisects 2 angles
Arc Length
(A/360) = (l/(2πr))
Equation of a circle
(x - h)^2 + (y - k)^2 = r^2