Quadrilaterals and
their Properties
Unit 7: Activity 15
Quadrilaterals & their Properties
Date Learning Target
11/14 Bisectors of Triangles
11/17 Kites and Midsegments
Page
#
78
82
Quadrilaterals & their Properties
Learning Task:
I will develop the properties of kites
and apply the Triangle Midsegment
Theorem.
Quadrilaterals & their Properties
B
Terms to know…
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Opposite Sides
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Consecutive Sides
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Opposite Angles
A
C
D
Consecutive Angles
Quadrilaterals & their Properties
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Kite - quadrilateral with exactly two distinct
pairs of congruent consecutive sides
Quadrilaterals & their Properties
Properties of Kites
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Exactly two pairs of consecutive sides are congruent
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One diagonal divides a kite into two congruent triangles
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The diagonals of a kite are perpendicular
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The other diagonal divides a kite into two isosceles triangles
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One pair of opposite angles are congruent angles (nonvertex angles)
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One diagonal bisects a pair of opposite angles (vertex
angles)
Quadrilaterals & their Properties
Midsegment - segment whose endpoints are the
midpoints of two sides of a triangle
Triangle Midsegment Theorem
The midsegment of a
triangle is parallel to the
third side and its length is
one-half the length of the
third side
Quadrilaterals & their Properties
Date
11/14
11/17
11/18
Learning Target
Bisectors of Triangles
Kites and Midsegments
Trapezoids
Page
#
78
82
84
Quadrilaterals & their Properties
Learning Task:
I will develop and apply the
properties of trapezoids.
Quadrilaterals & their Properties
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Trapezoid - quadrilateral with exactly one
pair of parallel sides
Base
Base Leg
Angle
Leg
Base
Quadrilaterals & their Properties
Median - segment whose endpoints are the midpoints of
the two legs of the trapezoid
Trapezoid Median Theorem
The median of a
trapezoid is parallel to
both bases and its length
is the average of the
bases
Quadrilaterals & their Properties
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Isosceles Trapezoid - trapezoid with
congruent legs
Quadrilaterals & their Properties
Properties of Trapezoids
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One pair of parallel sides (bases)
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Median is the average of the bases
Properties of Isosceles Trapezoids
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Congruent legs
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Congruent base angles
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Congruent diagonals
Quadrilaterals & their Properties
Date
11/14
11/17
11/18
11/28
Learning Target
Bisectors of Triangles
Kites and Midsegments
Trapezoids
Parallelograms
Page
#
78
82
84
86
Quadrilaterals & their Properties
Learning Task:
I will develop and apply the
properties of parallelogram.
Quadrilaterals & their Properties
❖
Parallelogram - quadrilateral with both pairs
of opposite sides parallel.
Quadrilaterals & their Properties
Properties of Parallelograms
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Opposite sides are parallel
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Opposite sides are congruent
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Opposite angles are congruent
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Consecutive angles are supplementary
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Diagonals bisect each other
Quadrilaterals & their Properties
Date
11/14
11/17
11/18
11/28
11/29
Learning Target
Bisectors of Triangles
Kites and Midsegments
Trapezoids
Parallelograms
Rectangles, Rhombi & Squares
Page
#
78
82
84
86
88
Quadrilaterals & their Properties
Learning Task:
I will develop and apply the
properties of rectangles, rhombi
and squares.
Quadrilaterals & their Properties
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Rectangle - parallelogram with four right
angles
Quadrilaterals & their Properties
Properties of Rectangles
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All the properties of parallelograms
apply
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All angles are right angles
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Congruent diagonals
Quadrilaterals & their Properties
❖
Rhombus - parallelogram with four congruent
sides
Quadrilaterals & their Properties
Properties of Rhombi
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All the properties of parallelograms apply
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All sides are congruent
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Diagonals bisect the angles
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Diagonals are perpendicular bisectors of
each other
Quadrilaterals & their Properties
❖
Square - parallelogram with four congruent
sides and four right angles
Quadrilaterals & their Properties
Properties of Square
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All the properties of parallelograms apply
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All the properties of rectangle apply
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All the properties of rhombi apply
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All sides are congruent
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All angles are right angles
Quadrilaterals & their Properties
HOMEWORK
p. 221, problems 1-10,13
Due Thursday
Quadrilaterals & their Properties