GEOMETRY VOLUME AND SURFACE AREA FORMULAS

33 terms by harrypotter_cool

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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

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