Theorems

Assorted Theorems

Line Intersection Theorem: Two different lines intersect in at most one point.
Betweenness Theorem: If C is between A and B and on line segment AB, then AC + CB = AB.

Related Theorems

Theorem: If A, B, and C are distinct points and AC + CB = AB, then C lies on line segment AB.
Theorem: For any points A, B, and C, AC + CB is greater than or equal to line segment AB .
Pythagorean Theorem: a2 + b2 = c2, if c is the hypotenuse.
Right Angle Congruence Theorem: All right angles are congruent.

Perimeter/Circumference and Area Theorems

Theorem: Circumference of a Circle: 2 p r
OR
Theorem: Circumference of a Circle: p d

Theorem: Area of a Circle: 2 p r2

Theorem: Area of a Trapezoid: A= 1/2h(b1+b2)

Theorem: Area of a Triangle: A= 1/2bh

Theorem: Area of a Square: A= s2

Theorem: Area of a Paralellogram: A= bh

Theorem: Area of a Rhombus: A= 1/2d1d2

Theorem: Area of a Kite: A= 1/2d1d2

Theorem: Area of a Regular Polygon: A= 1/2aP

Theorem: Area of a Equilateral Triangle: A= 1/4(the square root of 3)(s2)

Theorem: Area of a Sector: A= measure of arc AB/360 p r2

Theorem: Area of Similar Polygons Theorem: If two polygons are similar w/corresponding sides in the ratio of a:b, then the ration of their areas is a2:b2.

Theorem: Euler's Theorem: F + V = E + 2 (F= number of faces; V= number of vertices; E= number of edges)

Theorem: Surface Area of a Right Prism: S= 2B + Ph (B= base area; P= perimeter of the base; h= height)

Theorem: Surface Area of a Right Cylinder: S= 2 p r2 + 2 p> rh

Theorem: Surface Area of a Regular Pyramid: S= B + 1/2Pl (l= slant height)

Theorem: Surface Area of a Right Cone: S= p r2 + p rl

Theorem: Surface Area of a Sphere: S= 4 p r2

Volume