LESSON 6.1
CLASSIFYING QUADRILATERALS
OBJECTIVE:
To define and classify special
types of quadrilaterals
1
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
NO PAIRS OF PARALLEL SIDES
quadrilateral is a four-sided polygon.
A ___________
kite is a quadrilateral with two
A ____
pairs of adjacent sides  and no
opposite sides .
2
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
1 PAIR OF PARALLEL SIDES
trapezoid is a quadrilateral with
A __________
exactly 1 pair of parallel sides.
isosceles trapezoid is a
An __________________
trapezoid whose nonparallel sides
are .
3
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
2 PAIRS OF PARALLEL SIDES
parallelogram is a quadrilateral with both pairs
A _____________
of opposite sides parallel.
rhombus is an equilateral parallelogram.
A _________
rectangle is an equiangular parallelogram.
A _________
4
square is an equilateral and equiangular
A _______
Slide Courtesy of Miss Fisher
parallelogram.
Modified by McConaughy 1/28/08
Page Modified on
1/28/08
True or false: A square is a
rectangle and a rhombus. Explain.
Special Quadrilaterals
kites
5
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
Properties of Parallelograms:
Angles
Use Same-Side Interior Angle Theorem to find
the missing angles in the parallelogram below:
a
120
The consecutive angles in a
The opposite angles in a
6
b
c
supplementary
are _____________.
congruent
are _____________.
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
Check for Understanding: Summary
Properties of Parallelograms
Opposite sides are _________________. (DEF.)
Opposite sides are _________________.
Opposite angles are ________________.
Consecutive angles are _____________>
7
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
Check for Understanding:
Properties of Special Quadrilaterals
Parallelogram
Rhombus
Equilateral
Equiangular
Opp. Sides //
Opp. Sides =
Opp. Angles =
8
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
Rectangle
Square
EXAMPLE #1
U
In parallelogram RSTU,
mR = 2x – 10 and
mS = 3x + 50. Find x.
R
T
S
Def of Parallelogram
RU || ST
mR + mS = 180
2x – 10 + 3x + 50 = 180
5x + 40 = 180
5x = 140
SSI
Substitution
Simplify
Subt prop of =
Alert! Consecutive angles of a parallelogram are
Div prop of =
x = 28
supplementary.
9
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
EXAMPLE #2
L
Find the values of the variables in
the rhombus. Then find the lengths
of the sides.
Find a.
5a + 4 = 3a + 8
2a = 4
a=2
Find b.
4b – 2 = 3b + 2
b=4
10
3b + 2
5a + 4
N
3a + 8
S 4b – 2 T
LN = 3b + 2 = 3(4) + 2 = 14
ST = 4b – 2 = 4(4) – 2 = 14
LS = 5a + 4 = 5(2) + 4 = 14
NT = 3a + 8 = 3(2) + 8 = 14
Alert! Opposite sides
of a ofparallelogram
are congruent.
Slide Courtesy
Miss Fisher
Modified by McConaughy 1/28/08
Classifying Quadrilaterals
During this lesson, you will classify quadrilaterals
algebraically by using Distance Formula and
Slope Formula.
11
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
Algebra Review
Two lines which have the same slope are
_____________
to each other.
parallel
Two lines whose slopes are negative
(opposite) reciprocals are
___________________
to each other.
perpendicular
Given two points (x1, y1) and (x2, y2), write:
Slope Formula: ____________________
Distance Formula:__________________
12
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
EXAMPLE #3
Determine the most precise name for the
quadrilateral with vertices A(-3,3), B(2,4), C(3,-1)
and D(-2,-2).
1.
Graph quadrilateral ABCD.
B
A
D
13
C
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08
EXAMPLE #3
Determine the most precise name for the
quadrilateral with vertices A(-3,3), B(2,4), C(3,-1)
and D(-2,-2). Explain your response.
2.
Find the slope of each side.
4–3
1
AB || CD and BC || DA
=
2 – (-3)
5
b/c same slope
Slope BC = -1 – 4 = -5 = -5
3–2
1
Slope AB =
-2 – (-1) = -1 = 1
-2 – 3
-5 5
Slope DA = 3 – (-2) = 5 = -5
Slide
Courtesy of -1
Miss Fisher
-3
–
(-2)
14
Modified by McConaughy 1/28/08
Slope CD =
AB  DA, AB  BC,
CD  DA and
CD  BC b/c
opposite reciprocal
slopes
EXAMPLE #3
Determine the most precise name for the
quadrilateral with vertices A(-3,3), B(2,4), C(3,-1)
and D(-2,-2).
2.
Find the length of each side.
AB = (2  (3)) 2  (4  3) 2 = 25  1 = 26
BC =
(3  2) 2  ( 1  4) 2
= 25  1 = 26
CD = (2  3) 2  (2  (1)) 2 = 25  1 = 26
DA = (3  (2)) 2  (3  (2)) 2 =
25  1
= 26
All sides have the same length.
15
Slide Courtesy
of Miss
The most precise
name
forFisher
the quad is a square.
Modified by McConaughy 1/28/08
ASSIGNMENT
Pg 290 #1-13 (graph paper needed
for #13), 20-24 even, 37-42
16
Slide Courtesy of Miss Fisher
Modified by McConaughy 1/28/08