Parallelograms

decagon

10 sides

dodecagon

12 sides

hexagon

6 sides

regular

sides and angles are congruent and convex

Polygon Interior angles theorem

the sum of all measures in an n-gon is (n-2)x180

Interior angles of a quadrilateral

sum is 360

Polygon exterior angles theorem

sum of all exterior angles is 360

Parallelogram opposite sides theorem

If its a parallelogram then opposite sides are congruent

parallelogram opposite angles theorem

parallelogram opposite angles are congruent

parallelogram consecutive angles theorem

parallelogram consecutive angles sum to 180

parallelogram diagnols theorem

parallelogram diagnols bisect eachother

Opposite sides parallel and congruent theorem

One pair of opposite sides are congruent and parallel

Rhombus

A parallelogram with 4 congruent sides

Rectangle

A parallelogram with 4 right angles

square

a parallelogram with 4 congruent sides and 4 right angles

Rhombus Diagnols Theorem

A parallelogram is a rhombus only if its diagnols are perpendicular

Rhombus opposite angles theorem

A parallelogram is a rhombus only if the diagnols bisect a pair of opposite angles

Rectangle diagnols theorem

A parallelogram is a rectangle only if the diagnols are congruent

Kite

a quadrilateral that has 2 pairs of consecutive conguent sides.

Opposite sides are not congruent

Kite diagnols theorem

If its a kite then the diagnols are perpendicular

Kite opposite angles theorem

If its a kite then ONE PAIR of opposite angles are congruent

Trapezoid

Quadrilateral with 1 pair of parallel sides the bases

2 pairs of base Angles

Legs- nonparallel sides

Isosceles Trapazoid

Trapazoid when both legs are congruent

Isoceles Trapazoid Base Angles Theorem

If a trapezoid is isosceles then each base Angle pair is congruent

Isosceles Trapazoid Base angles converse

If a trapezoid has 1 PAIR of congruent base angles then its an isoceles trapezoid

Isosceles Trapezoid Diagnols Theorem

A trapezoid is only isosceles if the diagonals are congruent

Midsegment

A segment that connects the midpoints of trapezoid legs

Trapezoid Midsegment theorem

The midsegment is parallel to each base

Its is half the SUM of the base lengths