Transcript 2) all sides are congruent

Quadrilaterals

ANY four-sided closed figure is a quadrilateral.
Rules of a Quadrilateral

If a shape has four-sides and is closed then it is
a quadrilateral

Therefore:



There will be four sides
There will be four angles
The sum of the four angles is 360 degrees
How do we know this to be true?

How can we be sure that the four angles in
quadrilaterals add up to 360 degrees?

Because all quadrilaterals can be cut into two
triangles BY DRAWING DIAGONALS

One triangle (180 degrees) plus another triangle (180
degrees) equals a quadrilateral (360 degrees)
How do we know this to be true?

How can we be sure that the four angles in
quadrilaterals add up to 360 degrees?

Because all quadrilaterals can be cut into two
triangles BY DRAWING DIAGONALS

One triangle (180 degrees) plus another triangle (180
degrees) equals a quadrilateral (360 degrees)
Special Quadrilaterals

Parallelogram

A parallelogram is a special kind of quadrilaterals
where both pairs of opposite sides are parallel.
Rules of a Parallelogram

If a quadrilateral is a parallelogram then the
following is true:

1) Opposite sides are congruent

2) Opposite angles are congruent
Examples of Parallelograms

Here are some types of parallelograms that you
may already be familiar with:
Rhombus:
1) Opposite Sides are Parallel
2) ALL SIDES ARE
CONGRUENT
3) Opposite angles are
congruent
Examples of Parallelograms

Here are some types of parallelograms that you
may already be familiar with:
Rectangle:
1) Opposite Sides are Parallel
2) Opposite Sides are Congruent
3) FOUR RIGHT ANGLES
Examples of Parallelograms

Here are some types of parallelograms that you
may already be familiar with:
Square:
1) Opposite Sides are Parallel
2) ALL SIDES ARE CONGRUENT
3) FOUR RIGHT ANGLES
Two Pairs of Parallel Sides

A Rhombus, a rectangle, and a square, are all
parallelograms because they have two pairs of
parallel sides.
But what do we call a quadrilateral that only has
one pair of parallel sides?
Trapezoid

A trapezoid is a quadrilateral with only one pair
of parallel sides.
Rules of a Trapezoid

If a quadrilateral is a trapezoid then the
following are true:

1) There is exactly one pair of parallel sides.
Special Trapezoids

Isosceles Trapezoid

An isosceles trapezoid is a trapezoid that has
congruent non-parallel sides.
Rules of Isosceles Trapezoids

If a Trapezoid is an isosceles trapezoid then the
following is true:

1) There is exactly one pair of parallel sides

2) The NON-PARALLEL sides are congruent

3) There will be TWO PAIRS of congruent angles
Quadrilateral Family Tree
Quadrilateral
Trapezoid
Parallelogram
Isosceles Trapezoid
Rhombus
Rectangle
Square