# Geometry Theorems, Formulas, and Concepts

Classified in Mathematics

Written at on English with a size of 3.79 KB.

## Polygon Interior Angles Theorem

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

### Interior angles of a quadrilateral:

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

## 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)

## Theorems

### If a quadrilateral is a parallelogram, then its opposite sides are congruent

### If a quadrilateral is a parallelogram, then its opposite angles are congruent

### If a quadrilateral is a parallelogram, then its consecutive angles are supplementary

### If a quadrilateral is a parallelogram, then its diagonal bisects each other

### If both pairs of opposite sides of a quadrilateral are congruent, if both pairs of opposite angles of a quadrilateral are congruent, if one pair of opposite sides of a quadrilateral are congruent and parallel, and If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

## 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*=√(*x*2−*x*1)2+(*y*2−*y*1)2

### Slope Formula

*m*=(*x*1−*x*2 ) / (*y*1−*y*2)

### Pythagorean Theorem

*c*=*a*2+*b*2 (hypotenuse)^{2}=(leg^{2})+(leg^{2})

### Area triangle

1/2xbasexheight

### Hypotenuse 45-45-90

= legx√**2 **

### Hypotenuse 30-60-90

= 2xshorter leg

### Longer leg

= shorter leg x √**3 **

### tan= opposite/adjacent

### cos=adjacent/hypotenuse

**sin= ***opposite/hypotenuse Inverse tan= tan ^{-1 }Inverse sine = sin^{-1}Inverse Cosine= cos^{-1`}*

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