1. Classifying Quadrilaterals
Lesson 6-1
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.
6-1

2. Classifying Quadrilaterals
Lesson 6-1
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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3. Classifying Quadrilaterals
Lesson 6-1
Notes
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4. Classifying Quadrilaterals
Lesson 6-1
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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5. Classifying Quadrilaterals
Lesson 6-1
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 = slope of BH = slope of HA = slope of QA =
9 – 4
–2 – (–4) 5 2 =
9 – 9
8 – (–2)
4 – 9
10 – 8
= –
4 – 4
–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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6. Classifying Quadrilaterals
Lesson 6-1
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 = = 29
BH = (8 – (–2))2 + (9 – 9)2 = = 10
QA = (– 4 – 10)2 + (4 – 4)2 = = 14
Because QB = HA, QBHA is an isosceles trapezoid.
Quick Check
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7. Classifying Quadrilaterals
Lesson 6-1
Additional Examples
Using the Properties of Special Quadrilaterals
In parallelogram RSTU, m R = 2x – 10 and
m S = 3x Find x.
Draw quadrilateral RSTU. Label R and S.
RSTU is a parallelogram.
Given
Definition of parallelogram
ST || RU
m R + m S = 180
If lines are parallel, then interior
angles on the same side of a
transversal are supplementary.
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8. Classifying Quadrilaterals
Lesson 6-1
Additional Examples
(continued)
(2x – 10) + (3x + 50) = 180
Substitute 2x – 10 for m R and
3x + 50 for m S.
5x + 40 = 180
Simplify.
Subtract 40 from each side.
5x = 140
x = 28
Divide each side by 5.
Quick Check
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9. Classifying Quadrilaterals
Lesson 6-1
Lesson Quiz
Judging by appearance, classify the quadrilaterals in Exercises 1
and 2 in as many ways as possible. 1. 2.
quadrilateral, kite
quadrilateral, parallelogram,
rectangle, rhombus, square
4. What is the most precise name
for the figure in Exercise 2?
3. What is the most precise name
for the figure in Exercise 1?
square
kite
5. Find the values of the variables
in the rhombus to the right.
a = 60, x = 6, y = 2
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