Download Section 6.3 Rectangles

Rectangles.notebook
November 28, 2011
Section 6.3 Rectangles
Given a quadrilateral you will be
able to identify and use the
properties of rectangles
to solve problems.
Nov 25­11:41 AM
Find the value for y.
Bell Ringer #2
B
A
3Y
y
Y
D
3y + y = 180
4y = 180
y = 45
C
Find the value for <B.
A
3Y
D
B
<B
Y+30
C
3y = y + 30
2y = 30
y = 15
<B = 3(15)
<B = 45
Jul 26­3:02 PM
1
Rectangles.notebook
November 28, 2011
Rectangles
Parallelogram with four
right angles.
Jul 26­2:50 PM
Theorem
If a parallelogram is a rectangle,
then its diagonals are congruent.
Jul 26­3:06 PM
2
Rectangles.notebook
November 28, 2011
Remember Parallelogram properties
A
B
<BCD ≅ <BAD
<ABC ≅ <CDA
E
BE=DE
AE = CE
AD||BC
C
D
AB||CD
Jul 26­3:08 PM
MO = 2x-8; NP = 23
Find the value for x
M
N
C
P
x
2x - 8 = 24
2x = 32
x = 16
O
Jul 26­3:09 PM
3
Rectangles.notebook
November 28, 2011
Summary of Rectangle Properties
Opposite Sides are
congruent & parallel
Opposite angles are congruent
Consecutive angles are supplementary
Diagonals are congruent and
bisect each other
All four angles are right
Jul 26­3:11 PM
CN = x+21; CO = 3x+11
Find the value for x
M
x
C
P
N
Diagonals are congruent,
and bisect each other
x+21 = 3x+11
10 = 2x
5=x
O
Jul 26­3:35 PM
4
Rectangles.notebook
November 28, 2011
MO = 4x-13; PC = x+7
Find the value for x
M
N
C
x + 7 + x + 7 = 4x - 13
2x + 14 = 4x - 13
27 = 2x
13.5 = x
x
O
P
Jul 26­3:38 PM
If quadrilateral MNOP is a rectangle
What type of triangle is NCO?
What type of triangle is MCN?
M
N
C
O
P
Jul 26­4:12 PM
5
Rectangles.notebook
November 28, 2011
If <MCN = 100,
What is m<CMN?
M
N
C
O
P
Jul 26­4:12 PM
Check Your Understanding
1
What is the measure of segment AE if AE = (5x – 3) cm and ED = (15 – x) cm?
A 12
B
A B
24
C
E
48
D Insufficient information
C D
Select the correct answer.
Check Your Understanding
6
Rectangles.notebook
November 28, 2011
Check Your Understanding
2 Quadrilateral ABCD is a parallelogram. What is the measure of the angle D?
A 70°
B
130°
C
110°
D Insufficient data
Select the correct answer.
Check Your Understanding
Check Your Understanding
3 Parallelogram ABCD is a Rectangle. What is the value of the x?
A 70°
B
130°
C
110°
x + 20
D Insufficient data
Select the correct answer.
Check Your Understanding
7
Rectangles.notebook
November 28, 2011
Check Your Understanding
4 Diagonals of a rectangle bisect each other.
A. True
B. False
Select the correct answer.
Check Your Understanding
Check Your Understanding
5 Which of the following statements apply to this image?
A AB = BC
B AC ≠ BD
A B
C AC = BD
D AD = DC
D C
Select the correct answer.
Check Your Understanding
8
Rectangles.notebook
November 28, 2011
Nov 25­11:40 AM
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