# math

Classified in Mathematics

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*Chapter 8* 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) Theorem: If a quadrilateral is a parallelogram, then its **opposite** sides are **congruent** Theorem: If a quadrilateral is a parallelogram, then its opposite angles are congruent.Theorem: If a quadrilateral is a parallelogram, then its consecutive angles are supplementaryTheorem: If a quadrilateral is a parallelogram, then its diagonal bisects each other. Theorem: 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.

Chapter 7 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.Chapter 6: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.*

*Chapter 4 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)2Slope 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`}*