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.

1. Four-sided polygon

QUADRILATERAL

1.

2.

3.

4.

PARALLELOGRAM

2.

3.

1. 1.

2.

3.

1.

2.

3.

1.

2.

ISOSCELES TRAPEZOID

Parallelogram

Parallelogram

Parallelogram

1

2

Parallelogram

1

2

Parallelogram

1

23

4

Parallelogram

1

23

4

Parallelogram

1

23

4

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?

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.

1. Four-sided polygon

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.

1. Four-sided polygon

QUADRILATERAL

2. Opposite angles are congruent

3.

4.

PARALLELOGRAM

2.

3.

1. 1.

2. 3.

1.

2.

1. Opposite sides are congruent 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.

1. Four-sided polygon

QUADRILATERAL

2. Opposite angles are congruent

3. Diagonals bisect each other

4.

PARALLELOGRAM

2.

3.

1. 1.

2. 3.

1.

2.

1. Opposite sides are congruent 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.

1. Four-sided polygon

QUADRILATERAL

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

2.

3.

1. 1.

2. 3.

1.

2.

1. Opposite sides are congruent 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

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

SQUARE

2. All properties above

3.

1. Four right angles

RECTANGLE1.

2. 3.

4.

1.

2.

3.

1. Opposite sides are congruent 2.

3.

1.

Rectangle•What should be true about the overlapping

triangles formed by the diagonals?

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

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

SQUARE

2. All properties above

3. Diagonals are congruent

1. Four right angles

RECTANGLE1.

2. 3.

4.

1.

2.

3.

1. Opposite sides are congruent 2.

3.

1.

Rhombus•A quadrilateral with four congruent sides

Rhombus•Also has all the properties of a parallelogram

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

SQUARE

2. All properties above

3. Diagonals are congruent

1. Four right angles

RECTANGLE1. Four congruent sides

2. All properties above3.

4.

RHOMBUS

1.

1. Opposite sides are congruent 2.

3.

1.

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

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

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

Rhombus•Each diagonal bisects a pair of opposite angles

Rhombus•Each diagonal bisects a pair of opposite angles

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

SQUARE

2. All properties above

3. Diagonals are congruent

1. Four right angles

RECTANGLE1. Four congruent sides

2. All properties above

3. Diagonals bisect opposite angles

4.

RHOMBUS

1.

1. Opposite sides are congruent 2.

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?

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

SQUARE

2. All properties above

3. Diagonals are congruent

1. Four right angles

RECTANGLE1. Four congruent sides

2. All properties above

3. Diagonals bisect opposite angles

4. Diagonals are

RHOMBUS

1.

1. Opposite sides are congruent 2.

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

2. All properties above

3. Diagonals are congruent

1. Four right angles

RECTANGLE

1. Four congruent sides

2. All properties above

3. Diagonals bisect opposite angles

4. Diagonals are

RHOMBUS

1.

3.

2. All properties of a rhombus

ParallelogramsParallelograms

RectanglesRectangles RhombusesRhombuses

SquaresSquares

1.

TRAPEZOID

1. Four-sided polygonQUADRILATERAL

1. Opposite sides are congruent

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supplementary

PARALLELOGRAM

2. Properties of a rhombus

1. Properties of a rectangle

SQUARE

2. Four right angles

3. Diagonals are congruent

1. All properties of a parallelogram

RECTANGLE1. Properties of a parallelogram

2. All sides are congruent

3. Diagonals are perpendicular

4. Diagonals bisect opposite angles

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

1. Four-sided polygon

QUADRILATERAL

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

2. All properties above

3. Diagonals are congruent

1. Four right angles

RECTANGLE

2. All properties above

3. Diagonals bisect opposite angles

1.

2.

1. Opposite sides are congruent

Trapezoid•If the legs are congruent, the trapezoid is

an isosceles trapezoid

1. One pair of parallel sides

TRAPEZOID

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

2. All properties above

3. Diagonals are congruent

1. Four right angles

RECTANGLE1. Legs are congruent

2.

3.

ISOSCELESTRAPEZOID

1. Opposite sides are congruent

Isosceles Trapezoid

Isosceles Trapezoid•In an isosceles trapezoid, the base angles

are congruent

1. One pair of parallel sides

TRAPEZOID

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

2. All properties above

3. Diagonals are congruent

1. Four right angles

RECTANGLE1. Legs are congruent

2. Base <s are congruent

3.

ISOSCELESTRAPEZOID

1. Opposite sides are congruent

Isosceles Trapezoid•What should be true about the diagonals

of an isosceles trapezoid?

Isosceles Trapezoid•What should be true about the diagonals

of an isosceles trapezoid?

1. One pair of parallel sides

TRAPEZOID

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

2. All properties above

3. Diagonals are congruent

1. Four right angles

RECTANGLE1. Legs are congruent

2. Base <s are congruent

3. Diagonals are congruent

ISOSCELESTRAPEZOID

1. Opposite sides are congruent

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

Trapezoid Midsegment

•Its length is the average of the two bases.

Trapezoid Midsegment

•Its length is the average of the two bases.

Kite•A quadrilateral with exactly two pairs of

congruent consecutive sides

1. Four-sided polygon

QUADRILATERAL

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

2. All properties above

1. Four right angles

RECTANGLE1. Four congruent sides

2. All properties above

3. Diagonals bisect opposite angles

RHOMBUS

KITE

1. Opposite sides are congruent2.

3.

1. 2 pairs of congruent consecutive sides

Kite•Diagonals are perpendicular

1. Four-sided polygon

QUADRILATERAL

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

2. All properties above

1. Four right angles

RECTANGLE1. Four congruent sides

2. All properties above

3. Diagonals bisect opposite angles

RHOMBUS

KITE

1. Opposite sides are congruent2. Diagonals are _

3.

1. 2 pairs of congruent consecutive sides

Kite•Exactly one pair of opposite angles are

congruent

1. Four-sided polygon

QUADRILATERAL

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supp.

PARALLELOGRAM

2. All properties above

1. Four right angles

RECTANGLE1. Four congruent sides

2. All properties above

3. Diagonals bisect opposite angles

RHOMBUS

KITE

1. Opposite sides are congruent2. Diagonals are _

3. One pair of opposite <scongruent

1. 2 pairs of congruent consecutive sides

1. Exactly one pair of parallel sides

TRAPEZOID

1. Four-sided polygonQUADRILATERAL

1. Opposite sides are congruent

2. Opposite angles are congruent

3. Diagonals bisect each other

4. Consecutive angles are supplementary

PARALLELOGRAM

2. Properties of a rhombus

1. Properties of a rectangle

SQUARE

2. Four right angles

3. Diagonals are congruent

1. All properties of a parallelogram

RECTANGLE1. Properties of a parallelogram

2. All sides are congruent

3. Diagonals are perpendicular

4. Diagonals bisect opposite angles

RHOMBUS

1. Exactly two pairs of congruent sides

2. Exactly one pair of congruent opposite angles

3. Diagonals are perpendicular

KITE

1. Legs are congruent

2. Diagonals are congruent

3. Two pairs of congruent base angles

ISOSCELES TRAPEZOID