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The Quadrilateral Family Tree. Wednesday 12/3/08 – Thursday 12/4/08. ________________________. 1. _____________________. __________. _____________________. 1. _____________________. _____________________. 1. _____________________. 2. _____________________. 1. _____________________. - PowerPoint PPT Presentation
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The Quadrilateral Family TreeWednesday 12/3/08 – Thursday 12/4/08
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3. _______________
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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
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