Unit 5: Rhombi, Rectangles, and Squares (6.4) p.347­355
Rhombus:
a parallelogram with 4 sides congruent
Rectangle:
a parallelogram with 4 right angles
Square:
a parallelogram with 4 congruent sides and 4 right angles
(both a rhombus and a rectangle)
Paralleograms
Rhombi
Rectangles
Squares
1
Rhombus Theorems (Facts)
Fact 1:
The Diagonals of a Rhombus are perpendicular ( )
A
B
AC BD if and only if ABCD is a Rhombus
D
C
Fact 2:
The Diagonals of a Rhombus bisect a pair of opposite angles
A
D
B
C
ABCD is a Rhombus if and only if AC bisects <DAB and <DCB and BD bisects <ABC and <ADC
2
Rectangle Theorem (Fact)
Fact 1:
A
D
The diagonals of a rectangle are congruent
B
C
ABCD is a rectangle if and only if AC≅BD
3
Example 1: Solve for x in each problem.
ABCD is a Square
A
EFGH is a Rhombus
D
E
H
11
7x + 19
10x0
F
C
B
12x ­ 5
QRST is a Rhombus
LMNO is a Rectangle
T
(4x ­ 36)0
L
(2x +10)0
O
X
M
G
Q
S
N
R
LX = 4x + 9
MO = 43
4
Prove that ABCD is a rectangle given the points: A(4,6), B(7,12), C(­1,16), and D(­4,10)
5
p. 351­352
#16­21 all
#33­44 all
#46
6