Theorem

Opposite sies of a parallelogram

Theorem

are congruent

Theorem

Opposite angles of a parallelogram

Theorem

are congruent

Theorem

Diagonals of a parallelogram

Theorem

bisect each other

Theorem

In a parallelogram, consecutive angles

Theorem

are supplementary

Theorem 

If both pairs of opposite sides of a quadrilateral are congruent, then

Theorem

the quadrilateral is a parallelogram

Theorem

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then

Theorem

the quadrilateral is a parallelogram

Theorem

If both pairs of opposite angles of a quadrilateral are congruent, then  

Theorem

the quadrilateral is a parallelogram

Theorem

If the diagonals of a quadrilateral bisect each other, then

Theorem

Then the quadrilateral is a parallelogram

Theorem

If the consecutive angles of a quadrilateral are supplementary, then

Theorem

the quadrilateral is a paralllelogram

1.  Both pairs of opposite sides are parallel

2.  Both pairs of opposite sides are congruent

3. One pair of opposite sides are parallel and congruent

4.  Both pairs of opposite angles are congruent

5.  The diagonals bisect each other

6.  All pairs of consecutive angles are supplementary

Theorem

If two lines are parallel, then

Theorem

all points on one line are equidistant from the other line

Theorem

If three parallel lines cut off congruent segments on one transversal, then

Theorem

 they cut off congruent segments on every transversal

Theorem

A line that contains the midpoint of one side of a triangle and is parallel to another side

Theorem

passes through the midpoint of the third side

Theorem

The segment that joins the midpoints of two sides of a triangle:

Theroem

2)  Is half as long as the third side

Rectangle

• a parallelogram with 4 right angles and 4 congruent sides
• it is a combination of both a rectangle and a rhombus

Theorem

The diagonals of a rectangle

Theorem

Theorem

The diagonals of a rhombus

Theorem

Theorem

Each diagonal of a rhombus

Theorem

bisects opposite angles

Theorem

The midpoint of the hypotenuse of a right triangle is

Theorem

is equidistant from the three vertices

Theorem

If an angle of a parallelogram is a right angle,

Theorem

then the parallelogram is a rectangle

Theorem

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If two consecutive sides of a parallelogram are congruent,

Theorem

then the parallelogram is a rhombus

Theorem

The base angles of an isosceles trapezoid

Theorem

 are congruent

Theorem

The median of a trapezoid:

Theorem

1)  is parallel to the bases

2)  has a length equal to the average of the bases

*m= 1/2(b1+b2)

(bases=the parallel sides of a trapezoid)