Geometry Theorems, Formulas, and Concepts

Classified in Mathematics

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Polygon Interior Angles Theorem

The sum of the measures of interior angles of an n-gon is (n-2)x180

The sum of the measures of the interior angles of a quadrilateral is 360o

Polygon Exterior Angles Theorem

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360.

Angles have to measure up to 360. 360/n (n=#of sides)

Rhombus

A quadrilateral is a rhombus only if it has four congruent sides.

A parallelogram is a rhombus if and only if its diagonals are perpendicular, if each diagonal bisects a pair of opposite angles.

Rectangle

A quadrilateral is a rectangle if and only if it has four right angles.

A parallelogram is a rectangle If and only if its diagonals are congruent.

Square

A quadrilateral is a square if and only it it is a rhombus and a rectangle.

Pythagorean Theorem

In a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

45-45-90 Theorem

The hypotenuse is √2 times as long as each leg

30-60-90 Theorem

In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg.

Perimeters of similar polygons

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

AA Similarity postulate

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

SSS Similarity Theorem

If the corresponding side lengths of two triangles are proportional, then the triangles are similar.

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180.

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the nonadjacent interior angles.

Formulas

Distance Formula

d=√(x2−x1)2+(y2−y1)2

Slope Formula

m=(x1−x2 ) / (y1−y2)

Pythagorean Theorem

c=a2+b2 (hypotenuse)2=(leg2)+(leg2)

1/2xbasexheight

= legx√

= 2xshorter leg

Longer leg

= shorter leg x √