The Quadrilateral Family Tree

The Quadrilateral Family TreeWednesday 12/3/08 – Thursday 12/4/08

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Quadrilateral

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1. Four-sided polygon

Parallelogram•A quadrilateral with two pairs of parallel sides

1.


QUADRILATERAL

1.

2.

3.

4.

PARALLELOGRAM

2.

3.

1. 1.

2.

3.

1.

2.

3.

1.

2.

ISOSCELES TRAPEZOID

Parallelogram

Parallelogram

1

2

Parallelogram

1

23

4

Parallelogram

1

23

4

•The two triangles formed by a diagonal are congruent by ASA.

Parallelogram

1

23

4

•What does that mean about opposite sides of a parallelogram?

1.

TRAPEZOID

1. Four-sided polygonQUADRILATERAL

1.

2.

3.

4.

PARALLELOGRAM

2.

1.

SQUARE

2.

3.

1.

RECTANGLE1.

2.

3.

4.

RHOMBUS

1.

2.

3.

KITE

1.

2.

3.

ISOSCELES TRAPEZOID

1.


QUADRILATERAL

2.

3.

4.

PARALLELOGRAM

2.

3.

1. 1.

2. 3.

1.

2.

1. Opposite sides are congruent 2.

3.

1.

Parallelograms•What about opposite angles in a

parallelogram?

1.


QUADRILATERAL

2. Opposite angles are congruent

3.

4.

PARALLELOGRAM

2.

3.

1. 1.

2. 3.

1.

2.


3.

1.

Parallelograms

1

2

•Are these two triangles congruent? By which postulate?

Parallelogram•Since the triangles are congruent, the diagonals

of the parallelogram bisect each other.

1.


QUADRILATERAL


3. Diagonals bisect each other

4.

PARALLELOGRAM

2.

3.

1. 1.

2. 3.

1.

2.


3.

1.

Parallelogram

5

6

•What kind of angles are angles 5 & 6?

Parallelogram•Consecutive angles in a parallelogram are

supplementary.

5

6

1.


QUADRILATERAL



4. Consecutive angles are supp.

PARALLELOGRAM

2.

3.

1. 1.

2. 3.

1.

2.


3.

1.

Rectangles, rhombuses, and squares

Rectangle•A quadrilateral with four right angles

Rectangle•Has all the properties of a parallelogram

1. 2. Opposite angles are congruent



PARALLELOGRAM

SQUARE

2. All properties above

3.

1. Four right angles

RECTANGLE1.

2. 3.

4.

1.

2.

3.


3.

1.

Rectangle•What should be true about the overlapping

triangles formed by the diagonals?

Rectangle•The triangles are congruent by SAS since

opposite sides of a parallelogram are congruent

Rectangle•So the diagonals in a rectangle must be

congruent by CPCTC

1. 2. Opposite angles are congruent



PARALLELOGRAM

SQUARE


3. Diagonals are congruent


RECTANGLE1.

2. 3.

4.

1.

2.

3.


3.

1.

Rhombus•A quadrilateral with four congruent sides

Rhombus•Also has all the properties of a parallelogram




PARALLELOGRAM

SQUARE




RECTANGLE1. Four congruent sides

2. All properties above3.

4.

RHOMBUS

1.


3.

1.

Rhombus•What kind of triangles are formed by a diagonal?

Rhombus•Each diagonal bisects a pair of opposite angles




PARALLELOGRAM

SQUARE






3. Diagonals bisect opposite angles

4.

RHOMBUS

1.


3.

1.

Rhombus

Rhombus•What should be true about angles 1 and 2?

12

Rhombus•What would the angle measures have to be?

12

Rhombus•What would the angle measures have to be?




PARALLELOGRAM

SQUARE







4. Diagonals are

RHOMBUS

1.


3.

1.

Square•A quadrilateral with four right angles (like

a rectangle) and four congruent sides (like a rhombus)

Square•So a square has all the properties of both

a rectangle and a rhombus

1. All properties of a rectangle

SQUARE




RECTANGLE

1. Four congruent sides



4. Diagonals are

RHOMBUS

1.

3.

2. All properties of a rhombus

ParallelogramsParallelograms

RectanglesRectangles RhombusesRhombuses

SquaresSquares

1.

TRAPEZOID


1. Opposite sides are congruent



4. Consecutive angles are supplementary

PARALLELOGRAM

2. Properties of a rhombus

1. Properties of a rectangle

SQUARE



1. All properties of a parallelogram

RECTANGLE1. Properties of a parallelogram

2. All sides are congruent

3. Diagonals are perpendicular


RHOMBUS

1.

2.

3.

KITE

1.

2.

3.

ISOSCELES TRAPEZOID

Trapezoid•A quadrilateral with exactly one pair of

parallel sides

1. One pair of parallel sides

TRAPEZOID


QUADRILATERAL




PARALLELOGRAM




RECTANGLE



1.

2.


Trapezoid•If the legs are congruent, the trapezoid is

an isosceles trapezoid


TRAPEZOID




PARALLELOGRAM




RECTANGLE1. Legs are congruent

2.

3.

ISOSCELESTRAPEZOID


Isosceles Trapezoid

Isosceles Trapezoid•In an isosceles trapezoid, the base angles

are congruent


TRAPEZOID




PARALLELOGRAM





2. Base <s are congruent

3.

ISOSCELESTRAPEZOID


Isosceles Trapezoid•What should be true about the diagonals

of an isosceles trapezoid?


TRAPEZOID




PARALLELOGRAM





2. Base <s are congruent


ISOSCELESTRAPEZOID


Trapezoid Midsegment•The segment formed by the midpoints of the legs

Trapezoid Midsegment

•Its length is the average of the two bases.

Kite•A quadrilateral with exactly two pairs of

congruent consecutive sides


QUADRILATERAL




PARALLELOGRAM






RHOMBUS

KITE

1. Opposite sides are congruent2.

3.

1. 2 pairs of congruent consecutive sides

Kite•Diagonals are perpendicular


QUADRILATERAL




PARALLELOGRAM






RHOMBUS

KITE

1. Opposite sides are congruent2. Diagonals are _

3.


Kite•Exactly one pair of opposite angles are

congruent


QUADRILATERAL




PARALLELOGRAM






RHOMBUS

KITE

1. Opposite sides are congruent2. Diagonals are _

3. One pair of opposite <scongruent


1. Exactly one pair of parallel sides

TRAPEZOID





4. Consecutive angles are supplementary

PARALLELOGRAM

2. Properties of a rhombus

1. Properties of a rectangle

SQUARE



1. All properties of a parallelogram

RECTANGLE1. Properties of a parallelogram

2. All sides are congruent



RHOMBUS

1. Exactly two pairs of congruent sides

2. Exactly one pair of congruent opposite angles


KITE

1. Legs are congruent


3. Two pairs of congruent base angles

ISOSCELES TRAPEZOID

The Quadrilateral Family Tree

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