1. 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

2. 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.

3. 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.

4. 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.

5. 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.

6. 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

7. 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.