Transcript 6.1 Classifying Quadrilaterals

6.1 Classifying Quadrilaterals
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- Classify quadrilaterals
1.6 Classifying Quadrilaterals
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What is a Quadrilateral?
A polygons with exactly four sides
Special Quadrilaterals
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Quadrilaterals with specific characteristics.
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Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Kite
Parallelogram
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Parallelogram: A Quadrilateral with
both pairs of opposite sides parallel
Rhombus
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Rhombus: A parallelogram with four
congruent sides
Rectangle
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Rectangle: A parallelogram with four
right angles
Square
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Square: A parallelogram with four
congruent sides and four right angles
(it is a rhombus and a rectangle)
A Square is a Regular Parallelogram
Kite
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Kite: A quadrilateral with two pairs of
consecutive congruent sides
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no opposite sides congruent
no parallel sides
Trapezoid
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Trapezoid: A quadrilateral with exactly
one pair of parallel sides
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Isosceles Trapezoid: Trapezoid with
legs (nonparallel sides) congruent
Quadrilateral Family Tree
Special Quadrilaterals
A parallelogram is a quadrilateral with both pairs
of opposite sides parallel.
A rhombus is a parallelogram with four
congruent sides.
A rectangle is a parallelogram with four right
angles.
A square is a parallelogram with four congruent
sides and right angles.
A kite is a quadrilateral with two pairs of adjacent
sides congruent and no opposite sides congruent.
A trapezoid is a quadrilateral with exactly one
pair of parallel sides. The isosceles trapezoid at
the right is a trapezoid whose nonparallel sides
(legs) are congruent.
Classifying Quadrilaterals
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Judging by appearance, classify each quadrilateral
in as many ways as possible:
Square
Rectangle
Rhombus
Parallelogram
Quadrilateral
Parallelogram
Quadrilateral
Classifying Quadrilaterals

Judging by appearance, classify each quadrilateral
in as many ways as possible:
Rhombus
Parallelogram
Quadrilateral
Trapezoid
Quadrilateral
Classifying Quadrilaterals

Judging by appearance, classify each quadrilateral
in as many ways as possible:
Rectangle
Parallelogram
Quadrilateral
Kite
Quadrilateral
Using Properties
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Find the value of the variables for the kite:
T
x+6
2y + 5
J
K
3x - 5
2x + 4
B
JB = KB
2x + 4 = 3x – 5
-x = -9
x=9
TK = 9 + 6
TK = 15
TJ => 2y + 5 = 15
2y = 10
y=5
Using Properties
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Find the values of the variables for the
rhombus:
3b + 2
5a + 4
3b + 2 = 4b -2
b=4
3a + 8
4b - 2
5a + 4 = 3a + 8
2a = 4
a=2
Lesson Quiz
Complete each statement.
1. A quadrilateral with four right angles is a
_________.
square or rectangle
2. A parallelogram with four right angles and four
congruent sides is a _______. square
3. A figure with 4 sides and 4 angles is a ______.
quadrilateral
4. Give the most descriptive name for this
quadrilateral. trapezoid
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