Download Classifying Quadrilaterals

Classifying Quadrilaterals
Lesson 6-1
Geometry
Notes
A quadrilateral is a polygon with four sides.
A parallelogram () is a quadrilateral
with both pairs of opposite sides parallel.
A rhombus is a  with four congruent sides.
A rectangle is a  with four right angles.
A square is a  with four congruent sides
and four right angles.
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Classifying Quadrilaterals
Lesson 6-1
Geometry
Notes
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.
An isosceles trapezoid is a trapezoid whose
nonparallel sides are congruent.
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Lesson
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Classifying Quadrilaterals
Lesson 6-1
Geometry
Notes
Lesson
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Lesson
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Classifying Quadrilaterals
Lesson 6-1
Geometry
Additional Examples
Classifying a Quadrilateral
Judging by appearance, classify ABCD in as many
ways as possible.
ABCD is a quadrilateral because it has
four sides.
It is a trapezoid because AB and DC appear
parallel and AD and BC appear nonparallel.
Quick Check
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Classifying Quadrilaterals
Lesson 6-1
Geometry
Additional Examples
Classifying by Coordinate Methods
Determine the most precise name for the quadrilateral with
vertices Q(–4, 4), B(–2, 9), H(8, 9), and A(10, 4).
Graph quadrilateral QBHA.
First, find the slope of each side.
slope of QB =
9–4
5
=
–2 – (–4)
2
slope of BH =
slope of HA =
9–9
=0
8 – (–2)
4–9
5
=
–
10 – 8
2
slope of QA =
4–4
=0
–4 – 10
BH is parallel to QA because their slopes are equal. QB is not parallel
to HA because their slopes are not equal.
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Classifying Quadrilaterals
Lesson 6-1
Geometry
Additional Examples
(continued)
One pair of opposite sides are parallel, so QBHA is a trapezoid.
Next, use the distance formula to see whether any pairs
of sides are congruent.
QB =
( –2 – ( –4))2 + (9 – 4)2 =
HA =
(10 – 8)2 + (4 – 9)2 =
BH =
(8 – (–2))2 + (9 – 9)2 =
100 + 0 = 10
QA =
(– 4 – 10)2 + (4 – 4)2 =
196 + 0 = 14
4 + 25 =
4 + 25 =
29
29
Because QB = HA, QBHA is an isosceles trapezoid.
Quick Check
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Classifying Quadrilaterals
Lesson 6-1
Geometry
Additional Examples
Using the Properties of Special Quadrilaterals
In parallelogram RSTU, m
m
R = 2x – 10 and
S = 3x + 50. Find x.
Draw quadrilateral RSTU. Label
RSTU is a parallelogram.
ST || RU
m R + m S = 180
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R and
S.
Given
Definition of parallelogram
If lines are parallel, then interior
angles on the same side of a
transversal are supplementary.
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Classifying Quadrilaterals
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Geometry
Additional Examples
(continued)
(2x – 10) + (3x + 50) = 180
5x + 40 = 180
5x = 140
x = 28
Substitute 2x – 10 for m R and
3x + 50 for m S.
Simplify.
Subtract 40 from each side.
Divide each side by 5.
Quick Check
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Classifying Quadrilaterals
Lesson 6-1
Geometry
Lesson Quiz
Judging by appearance, classify the quadrilaterals in Exercises 1
and 2 in as many ways as possible.
1.
2.
quadrilateral, parallelogram,
rectangle, rhombus, square
quadrilateral, kite
3. What is the most precise name
for the figure in Exercise 1?
kite
4. What is the most precise name
for the figure in Exercise 2?
square
5. Find the values of the variables
in the rhombus to the right.
a = 60, x = 6, y = 2
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