POLYGONS ( except Triangles) Polygon Interior angle sum The sum of the interior angle measures of an n-sided convex polygon is (n-2) 180 Polygon Exterior angle sum The sum of the exterior angle measures of a convex polygon, one angle at each vertex is 360 degrees

Parallelograms Theorems If the 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 parallelogram has one right angle, then it has four right angles.

If a quadrilateral is a parallelogram, then its diagonals bisect (divides into two equal parts) each other. If a quadrilateral is a parallelogram, then each diagonal separates the parallelogram into two congruent triangles.

Converse of Parallelogram theorems If both pairs of opposite side of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If both pairs of opposite angle of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If the diagonals of the quadrilateral bisect each other, then the quadrilateral is a parallelogram. If one pair of the opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram.

Special Parallelograms and their theorems Rectangle If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle Converse: If the parallelogram is a rectangle, then their the diagonals are congruent.

Rhombus and Square If a parallelogram is a rhombus, then its diagonals are perpendicular. If a parallelogram is a rhombus, then each diagonal bisects pair of opposite angles Converse: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a Rhombus. If the diagonal of a parallelogram bisects the opposite angles, then the parallelogram is a Rhombus If one pair of consecutive sides of a parallelogram are congruent, the parallelogram is a Rhombus If a quadrilateral is both a rectangle and a rhombus then, it is a Square

Trapezoids and Kites If a trapezoid is isosceles, then each pair of base angles is congruent. If a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid. A trapezoid is isosceles if its diagonals are congruent The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the length of the bases. If a quadrilateral is a kite, then its diagonals are perpendicular. If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.