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 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) 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 √2times 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=√(x2−x1)2+(y2−y1)2Slope Formula: m=(x1−x2 ) / (y1−y2) Pythagorean Theorem: c=a2+b2 (hypotenuse)2=(leg2)+(leg2)
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-1Inverse Cosine= cos-1`