Lesson 6-3
Rectangtes
Lesson 6-3: Rectangles
Rectangles
Definition: A rectangle is aparallelogram with four right angles.
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A rectangle is a special type of parallelogram.
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Thus a rectangle has all the properties of a parallelogram.
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.
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o
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.
Lesson 6-3: Rectangles
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Properties of Rectangles
Theorem: If a parallelogram is a rectangle, then its diagonals
are congruent.
Therefore, aAEB, aBEC, ICED, and aAED are isosceles triangles.
A
D
Converse: If the diagonals of aparallelogram
are congruent,
then the parallelogram is a rectangle.
Lesson 6-3: Rectangles
Examples.oo..o.
:
3x +2 and BE
1.
If AE
2.
If AC :21, then BE
^|
J.
4.
If m<l
:
If m<2:
:
:
4x and m<4
29, find the value of x.
x:9
units
10.5 uniJs
:2x,
40, find m<1,
find the value of
x.
m(3, m.-4, m<5 and m<6.
m<1:50,
m<3:40,
m<4:80,
m<5:100,
m<6:40
Lesson 6-3: Rectangles
x
:
18 units
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Nrfus zfu"z1
Name
Chapter 6: Quadlilaterals
Lesson 6-3: Rectangles
Classwork
Find the missing measurements of Rectangle ABCD.
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AB=16
BC=10
cD=tb
1()
A
M
,
to
AC=r8
lol
I
q
D
DA=
lb
\@-
re
l3=+
IF. f-#
BE=9
CE=
DE=
lto
5f m<ECD = Abo
# m<EAB = Vb"
lOf m<DEA = 72"
m<ABE = 36" m<EBC = 5+o m<BCE =
m<CDE =
m<EDA =
m<DAE =
m<AEB
m<CED =
l08o m<BEC =
=
bd
Sto
1t
BC=9
CD=14
DA= I
AC= 2o
DB=
ZO
AE=10
=
lO
CE= lO
DE= lO
m<ABE = lf
m<CDE
l5o
m<AEB = 150'
BE
=
lL+
D
m<EBC
m<EDA
m<BEC
IO
= -tro
=
=
-tzo
= /C
tf
n<ECD =
m<EAB=
15o mcDAE=
bo m<CED= 156o m<DEA= 3ct"
m<BCE
7f
3
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Chapter 6: Quadrilaterals
Lesson 6-3: Rectangles
Name:
Date:
Period:
Homewort
L Find the missin=e measurements of Rectangle ABCD.
AB =
118
BC = 63.5
CD =-]1L
DA = 6.5
AC = 7bY
DB = %rl
AE = 13+
BE = 134
cE= 13*
bls
lSLl
rn(ABE = 7X
m<cDE =Z{
mcAEB = l24'
OB =
o
m<EBC
m<EDA
rn<BEC
be.E
= lot
m<BCE
= fuo
m<DAE
m<CED
= bt
= bT
m<ECD
= lZlo
28o
m<EAB
m<DEA = 56'
= bt
Quadrilateral ABCD is a rectangle. Find the value of x.
2.
AE=18, AC=6x
J.
mZZ =38, mZl = 2x +18
4.
mZ5 = x, mZ6 =2x - 3O
5.
AD = l5x, BC = 3x + 144
6.
mZ2=67,m25= 2x-5
Use Rectangle LMNO and the given information
to find each measure.
7
.
If mZZ - 49', find m13.
8. lf mZI
=
63"
, ftnd mlL
9. If mZ4 =27', findmZl.
10. If mZ3
= 1 10', then
find mZ4.
= ZSo
=
HIJK is a parallelogram.
Deternrine if HIJK
is a recte
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the converse and
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rb ,,,?iJin.n rr rs a recrangte.
quadlilaterat has
r
I5' If a paralrerogram
has a g0" angre,
then
it is a rectangre.
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6-3: Self Check Quiz
Multiple Choice
Identify the choice that best completes the sftrtemenl or answers the question.
Quadrilateral ABCD is a rectangle.
AE
'4
^E
o
Its diagonals DB and AC intersect at point E.
T-- .!
1.
If DB :5x + 2 andAC
A4
B 11
c12
: 2x + 14, find the length of AE.
D22
T--=
2. If AB
:
AD
: 3x * 4, DC:7x - 16,
2y
1.24
-
6, BC
:
3y
-
13, what is the perimeter of ABCD?
tr^46
cs4
D76
f--l
3'
tr '/t:70o,
A
find the measure of
/5.
200
B 40'
C 70"
D
f--=
4'rc
1
10+
/rc:
30o, find the lneasure
of /3'
A 15o
B 3oo
c
75"
D 1o5o
f--=
5.lt ti =Zx-ZCr
A 30"
B 40"
c
D
60"
90"
and /'E
-
3r-gfJ,findthemeasure of
b
/1
'
,
Nu-a,
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6-3 Warmup
Numeric Response
ABCD is a rectangle.
n
tl
Find the value of x.
1.
AC= 38, nE= 2";c*5
I
2.
rn{t:18o, mfJ : l1tr-l/
I
3.
m{,t = (ti;r- lt1)", m./7: {l;,:*4j',
I
4' eE=3x+2,88= r+ 18