Download Rectangles - MazesMath

Aim: What are the properties of a rectangle
and how do we utilize them in solving
problems?
Do Now:
Aim: Properties of a Rectangle
Course: Applied Geo.
Properties of a Rectangle
A
A rectangle is a
parallelogram, one of whose
angles is a right angle.
B
E
C
D
Rectangle
Both pairs of opposite sides are parallel
Opposite angles are congruent
Consecutive angles are supplementary
The sum of the four angles is 3600
Opposite sides are congruent
PLUS, it has
Four right angles
Aim: Properties of a Rectangle
Course: Applied Geo.
Congruent diagonals that bisect each other
Model Problem
In rectangle ABCD, CB = 6, AB = 8, and AC
8
D
C
= 10.
5 E 5
6
Find the missing
lengths: 6
5
5
A
B
8
a. AD 6
b. CD 8
c. EC 5
d. AE 5
e. DE 5
f. DB 10
In a rectangle:
1) opposite sides are congruent, and
2) congruent diagonals bisect each other
CB = 6 = AD and AB = 8 = CD
AC = 10 = DB
1/2AC = 5 = AE = EC =Course:
DEApplied Geo.
Aim: Properties of a Rectangle
Model Problem
In rectangle ABCD, the length of diagonal
AC = 6x – 2, and the length of diagonal
D
BD = 4x + 2.
E
A. Find x:
B. Find AC and BD
A
B
In a rectangle, diagonals are congruent
AC  BD
C

6x – 2 = 4x + 2
2x – 2 =
+2
2x
=
4
x = 2
AC  BD = 6x – 2 = 4x + 2 = 4(2) + 2 = 10
Aim: Properties of a Rectangle
Course: Applied Geo.
Model Problem
Find the length of AD in rectangle ABCD, if
AB = 2 and diagonal BD = 4.
C
B
Pythagorean Theorem
4
2
a2 + b2 = c2
A
x
D
ABD is a right triangle
A rectangle has 4 right angles.
a2 + b2 = c2
22 + x2 = 42
4 + x2 = 16
x2 = 12
Aim: Properties of a Rectangle
x  12  3.46
Course: Applied Geo.
Model Problem
Find the value of x
M
N
Q
P
O
MQ = 2x – 1
NQ = x + 3
In a rectangle:
congruent diagonals bisect each other
x=4
Aim: Properties of a Rectangle
Course: Applied Geo.