=1(180)= =3(180)= =2(180)= =4 (180)=720

TheoremConverseHow to use If a quadrilateral is a parallelogram then its opposite sides are congruent. If the opposite sides are congruent and it is a quadrilateral then it is a parallelogramAB=CD BC=DA If a quadrilateral is a parallelogram, then its opposite angles are supplementary. If opposite angles are supplementary and it is a quadrilateral then it is a parallelogram <A=<C <B=<D If a quadrilateral is a parallelogram then its consecutive angles are supplementary If the consecutive angles of a quadrilateral are supplementary then the figure is a parallelogram m<A+m<B=180° m<B+m<C=180° m<C+m<D=180° m<D+m<A=180° If a quadrilateral is a parallelogram, then its diagonals bisect each other. If the diagonals bisect each other in a quadrilateral then it is a parallelogram AZ=CZ BZ=DZ B D C A C D A B B C D A B A D C Z

It has: One pair of opposite sides are congruent and parallel Both have pairs of opposite sides are congruent They have pairs of opposite angles are congruent An angle is supplementary to both of the consecutive angles When the diagonals bisect each other One pair of opposite sides are congruent and parallel Both have pairs of opposite sides are congruent They have pairs of opposite angles are congruent An angle is supplementary to both of the consecutive angles m<A+m<B=180° m<B+m<C=180° m<C+m<D=180° m<D+m<A=180° When the diagonals bisect each other

RhombusSquareRectangle is a parallelogram with four congruent sides and the diagonals are always perpendicular - if a quadrilateral is a rhombus then it is a parallelogram - if a parallelogram is rhombus then its diagonals are perpendicular - if a parallelogram is a rhombus then its diagonals bisect a pair of the opposite angles - if one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus Parallelogram with four congruent side and 4 right angles -All sides are congruent -Opposite sides are parallel -Diagonal are congruent -Bisect each other as right angles Parallelogram with 4 right angles -Diagonals bisect each other -Adjacent angles are supplementary -Diagonals are congruent -One pair of sides is congruent to each other

A C B D ABCD is parallelogram A B C D AC PERPENDICULAR BD <1CONGRUENT<2 A B C D AC is congruent to BD A B C D ABCD is parallelogram A B D C AC is congruent to BD

-Base angle are congruent -Midsegment length b1+b2/2 -Legs are congruent -Base angles are congruent -Diagonals are congruent Isosceles Trapezoid Thm. - If a quadrilateral is an isosceles then each pair of base angles are congruent -If the trapezoid has one pair of congruent base angles then the trapezoid is isosceles -A trapezoid is isosceles if only if its diagonals are congruent

Base angles Base Legs

A D C B <A is congruent <B <D is congruent <C A B C D AC is congruent to BD ABCD is isosceles A B C D

Quadrilateral with 2 pairs of adjacent and congruent sides -Diagonals are perpendicular -The longer diagonal always bisect the short diagonal -One pair of congruent opposite angles Kite Thm. -If a quadrilateral is a kite then diagonals are perpendicular -If a quadrilateral is a kite then exactly one pair of opposite angles are congruent.

Segment LN is congruent segment MO

A B C D <B is congruent <D

Area of Square: length x width Area of rectangle: base x height Area of triangle: base x height/2 Area of Parallelogram: base x height Area of a trapezoid: height/2 (base1 + base2) Area of a rhombus: base x height OR diagonal 1 x diagonal 2) Area of a kite: 1/2(diagonal 1 x diagonal2)

Area of Square: length x width x20= x10= x60=2700 Area of rectangle: length x width x59= x32=1568

Area of triangle: base x height/ x20/2=260