Math: Paralleogram/Rhombus/Rectange/Square/Kite/Isos Trapezoid
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5 Properties of Parallelograms?
 Both pairs of opposite sides are parallel
 Consecutive angles are supplementary
 Both pairs of opposite sides are congruent
 Both pairs of opposite angles are congruent
 Diagonals bisect each other

Parallelogram with four congruent sides
Rhombus

What is the rhombus theorem?
(2)
A parallelogram is a rhombus if and only if its diagonals are perpendicular
And
If each diagonal bisects a pair of opposite angles

8 Properties of a Rhombus?
 Both pairs of opposite sides are congruent
 Diagonals are perpendicular
 Diagonals bisect opposite angles
 Consecutive angles are supplementary
 Both pairs of opposite sides are congruent
 Both pairs of opposite angles are congruent
 Diagonals bisect each other
 Has all sides congruent

7 Properties of a Rectangle?
 Both pairs of opposite sides are parallel
 Diagonals are congruent
 Consecutive angles are supplementary
 Both pairs of opposite sides are congruent
 Both pairs of opposite angles are congruent
 Diagonals bisect each other
 Has all right angles

10 Properties for a Square?
 Both pairs of opposite sides are parallel
 Diagonals are perpendicular
 Diagonals bisect opposite angles
 Diagonals are congruent
 Consecutive angles are supplementary
 Both pairs of opposite sides are congruent
 Both pairs of opposite angles are congruent
 Diagonals bisect each other
 Has all right angles
 Has all congruent sides

A parallelogram that has all right angles
Rectangle

What is the theorem of a Rectangle?
A parallelogram is a rectangle if and only if its diagonals are congruent

What is the Corollary of a Rectangle?
A quadrilateral is a rectangle if and only if it has four right angles

What is a Square a combination of?
(3)
 Rhombus
 Parallelogram
 Rectangle

A parallelogram that has all sides congruent and all angles congruent
Square

What is the Square Corollary?
A quadrilateral is a square if and only if it is a rectangle AND a rhombus

True or False?:
Every rectangle is a square
False

True or False?:
Every square is a rectangle
True

True or False?:
Every rhombus is a parallelogram
True

True or False?:
Every parallelogram is a rectangle
False

True or False?:
Every rectangle is a parallelogram?
True

All quadrilaterals are equal to what?
360 degrees

The angles between the the 2 different sides are always...
Congruent

Theorem for a kite
If a quadrilateral is a kite then it has exactly 1 pair of opposite congruent angles and the diagonals are perpendicular

Quadrilateral that has 2 pair of congruent consecutive sides, but opposite sides are not congruent.
Kite

Kite:
What if the opposite sides were congruent?
It would be a rhombus

A quadrilateral having only one pair of parallel sides
Trapezoid

Isosceles trapezoids have congruent what?
Legs

What part is parallel in a Trapezoid?
The 2 bases

2 Theorems about Isosceles Trapezoids?
IF a trapezoid is isosceles then each pair of base angles are congruent
A trapezoid is isosceles if and only if its diagonals are congruent

A segment that joins the midpoints of the trapezoids legs.
Midsegment of a Trapezoid

The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases
Trapezoid Midsegment Theorem

Midsegment trapezoid theorem equation?
Midsegment=1/2(base1+base2)

Properties of Isos Trapezoid?
(3)
 Diagonals are congruent
 Base angles are congruent
 Has only 1 pair of opposite sides

The one property of Kites
Diagonals are perpendicular