Squares and
Rhombi
6.6
Properties of Special
Parallelograms
Objectives
1. Discover special properties of a
rectangle, rhombus, and square.
Properties of a
Rhombus
rhombus
-quadrilateral with four congruent sides
Properties of a Rhombus
Use the sides of your straight edge to
make two sets of intersecting parallel
lines
How do the lengths
compare?
Conjecture 56 – If two parallel lines are
intersected by a second pair of parallel
lines the same distance apart as the first
pair, then the parallelogram formed is a
rhombus.
Draw in the diagonals of the rhombus.
Use the corner of the patty paper to
see what kind of angles are formed.
C-57 The diagonals of a rhombus
are perpendicular
___________ _________
of
bisector
each other.
Use your patty paper to
compare the angles formed by
the diagonals.
C-58 The diagonals of a
rhombus _________
the angles
bisect
of the rhombus.
C-58 states that the diagonals bisect
each angle of the rhombus so…..
Foldable
* On the left hand
section, draw a
rhombus.
1. Opposite angles are congruent.
2. Consecutive angles are supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Diagonals make 2 congruent triangles.
1.Is a special type of parallelogram.
* On the right hand
side, list all of the
properties of a
rhombus.
2. Has 4 right angles
3. Diagonals are congruent.
1. Is A Special type of Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
Rhombus Properties
1. Is A Special type of Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
In addition to all the properties of a parallelogram, a rhombus
has two additional properties.
PROPERTY:
1. Opposite sides parallel.
2. Opposite sides congruent.
3. Opposite angles congruent.
4. Consecutive angles supplementary.
5. Diagonals bisect each other.
6. Four congruent sides.
7. Diagonals are perpendicular.
8. Diagonals bisect opposite angles.
PICTURE:
In addition to all the properties of a parallelogram, a rhombus
has two additional properties.
PROPERTY:
1. Opposite sides parallel.
2. Opposite sides congruent.
3. Opposite angles congruent.
4. Consecutive angles supplementary.
5. Diagonals bisect each other.
6. Four congruent sides.
7. Diagonals are perpendicular.
8. Diagonals bisect opposite angles.
PICTURE:
In addition to all the properties of a parallelogram, a rhombus
has three additional properties.
PROPERTY:
1. Opposite sides parallel.
2. Opposite sides congruent.
3. Opposite angles congruent.
4. Consecutive angles supplementary.
5. Diagonals bisect each other.
6. Four congruent sides.
7. Diagonals are perpendicular.
8. Diagonals bisect opposite angles.
PICTURE:
EXAMPLE 1
If mRST = 67, find mRSW.
S
T
W
R
V
mRSW=67/2
mRSW=33.5
Find mSVT if mSTV = 135.


S
T
135



W
R
V
How big is TVR?
45
mSVT=?
mSVT=45/2
mSVT=22.5
EXAMPLE 3
If mSWT = (2x + 8), find ‘x’.

S
T


W

R
V

What is the
mSWT?
90 degrees
2x + 8=90
2x=82
X=41
EXAMPLE 4
What is the value of ‘x’ if mWRV = (5x + 5) and
m WRS = (7x – 19)?





mWRV = mWRS
5x + 5 = 7x – 19
5=2x-19
24=2x
12=x
S
T
W
R
EXAMPLE 5
In rhombus DLMP, DM = 24, mLDO = 43,
and DL = 13. Find each of the following.










OM =
OM = 24/2=12
mDOL =
90
mDLO =
180-90-43=47
mDML =
43
DP =
13
L
D
O
P
M
Foldable
* Fold over the third
cut section and write
SQUARE on the
outside.
1. Opposite angles are congruent.
2. Consecutive angles are supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Diagonals make 2 congruent triangles.
1.Is a special type of parallelogram.
2. Has 4 right angles
3. Diagonals are congruent.
* Reopen the fold.
1. Is A Special type of Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
square
-parallelogram with four right
angles and four congruent sides
Foldable
* On the left hand
section, draw a square.
1. Opposite angles are congruent.
2. Consecutive angles are supplementary.
3. Opposite sides are congruent.
4. Diagonals bisect each other.
5. Diagonals make 2 congruent triangles.
1.Is a special type of parallelogram.
* On the right hand
side, list all of the
properties of a square.
2. Has 4 right angles
3. Diagonals are congruent.
1. Is A Special type of Parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
* Place in your
notebook and save for
tomorrow.
1. Is a parallelogram, rectangle, and
rhombus
2. 4 congruent sides and 4 congruent
(right) angles
Square Properties
1. Is a parallelogram, rectangle, and rhombus
2. 4 congruent sides and 4 congruent (right) angles
M
A
S
EXAMPLE 6
H
MATH is a square.
8
a)If MA = 8, then AT = ________
90
b)mHST = ________
c)mMAT = ________
90
4
4
d)If HS = 2, then HA = ________
and MT = ________
T
EXAMPLE 7
Use square ABCD and the given information to find each.
a)If mAED = (5x + 5), find ‘x’.
x = ________
A




mAED =90
5x + 5=90
5x=85
X=17
B
E
D
C
EXAMPLE 7
Use square ABCD and the given information to find each.
If mBAC = (5x), find ‘x’.
x = ________
A



mBAC =45
5x =45
X=9
B
E
D
C
Classwork/Homework