Ch 8.4
PROPERTIES OF RHOMBUSES,
RECTANGLES, AND SQUARES
WHAT IS A RHOMBUS?

A rhombus is a parallelogram that has four
congruent sides.

That means that the opposite sides must also
be parallel.

The diagonals of a rhombus form perpendicular
lines.
RHOMBUS CONT…

The diagonals bisect the interior angles.
RECTANGLES

A rectangle is a parallelogram with 4 right
angles.

Therefore, opposite sides must also be parallel.

The diagonals of a rectangle are congruent.
SQUARES

A square is a parallelogram with 4 right angles
AND 4 congruent sides.

Because a parallelogram has parallel opposite
sides, a square has parallel opposite sides.
TRAPEZOIDS

A trapezoid is a quadrilateral with 1 pair of
parallel sides.
CAN IT BE…?
Can any square be a rectangle?
 Yes!

Can any rectangle be a square?
 No!

Can any square be a rhombus?
 Yes!

Can any rectangle be a rhombus?
 No!
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SUPPOSE YOU HAVE A RHOMBUS ABCD… WHEN
ARE THE FOLLOWING TRUE? SOMETIMES,
NEVER, OR ALWAYS
B
A
m<A = m<C
C
m<B = m<C Sometimes
m<B = m<D
D
ALWAYS
AB = BC
AB = DC
ALWAYS
ALWAYS
ALWAYS
SUPPOSE YOU HAVE A RECTANGLE ABCD…
WHEN ARE THE FOLLOWING TRUE? ALWAYS?
NEVER? SOMETIMES?
A
B
M<A = m<C
ALWAYS
m<B = m<C ALWAYS
D
C
m<B = m<D
ALWAYS
AB = BC Sometimes
AB = DC
ALWAYS
ONE OF THESE IS NOT A RHOMBUS…
WHICH ONE IS NOT A RHOMBUS?
FIRST CLASSIFY THE QUADRILATERAL THEN
FIND X AND Y
Rhombus
5x + 6 = 8x
6 = 3x
2=x
< Q and < P should be supplementary!
12y – 1 + 97 = 180
12y + 96 = 180
12y = 84 y = 7
FIRST CLASSIFY THE QUADRILATERAL THEN
FIND X AND Y
Square
2x + 1 = 4x - 7
2x + 8 = 4x
8 = 2x
4=x
< KLN and < NLM should be complementary!
7y + 3 + 45 = 90
7y + 48 = 90
7y = 42
y =6
GIVEN THAT WXYZ IS A RHOMBUS…WHAT DO
WE KNOW ABOUT THE FIGURE?
The diagonals bisect the
interior angles.
12.5
56º
34º
56º
34º
12.5
34º
56º
56º
Z
12.5
Cos(56) = 7/x
7/Cos(56) = x
12.5 = x
SOH CAH TOA!
12.5
10.4
Y
A rhombus is a
parallelogram that has four
congruent sides.
That means that the
opposite sides must also
be parallel.
The diagonals of a
rhombus form
perpendicular lines.
THE FIGURE BELOW IS A RECTANGLE
FIND THE MISSING ANGLES AND SIDES
m<TPQ
m<PST
m<PTQ
PS
PR
HINT: PTQ is what kind of triangle?
LAPTOPS
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 Chapter 8-4
