Ch. 6.4 Rhombus, Why?
A Rhombus
is a type of
parallelogram.
It is a parallelogram
with 4
congruent sides
A Rhombus
is a type of
parallelogram.
A rhombus has ALL of the qualities of a parallelogram
Both pairs of opposite sides are parallel
►
►
A rhombus has ALL of the qualities of a parallelogram
Both pairs of opposite sides are congruent
A rhombus has ALL of the qualities of a parallelogram
A pair of opposite sides are both  II  and  ≅
►
►
A rhombus has ALL of the qualities of a parallelogram
Both pairs of opposite angles are congruent
◞
◞
◝
◟
◜
◜
A rhombus has ALL of the qualities of a parallelogram
Diagonals BISECT each other (cut each other in half)
A rhombus also
has these
special
properties...
 All four sides are congruent (the same)
A rhombus also
has these
special
properties...
Diagonals are perpendicular (form 90 degree angles)
A rhombus also
has these
special
properties...
Diagonals BISECT each  corner angle
34
∘
34
∘
56
∘
56
∘
56
∘
56
∘
34
34
∘
∘
Why is this a rhombus???
 All four sides are congruent (the same)
Diagonals are perpendicular (form 90  angles)
Diagonals BISECT each  corner angle
53
∘
53
∘
Why
is
this
a
rhombus???
 All four sides are congruent (the same)
Diagonals are perpendicular (form 90  angles)
Diagonals BISECT each  corner angle
22
22
22
22
Why
is
this
a
rhombus???
 All four sides are congruent (the same)
Diagonals are perpendicular (form 90  angles)
Diagonals BISECT each  corner angle
37
∘
5
5
Why is
this a rhombus???
 All four sides are congruent (the same)
Diagonals are perpendicular (form 90  angles)
Diagonals BISECT each  corner angle
A
32
32
∘
∘
B
58
∘
58
∘
58
∘
58
∘
D
32
32
∘
∘
C
Why
is
this
a
rhombus???
 All four sides are congruent (the same)
Diagonals are perpendicular (form 90  angles)
Diagonals BISECT each  corner angle
4y
4y
62
4y
∘
4y
Why
is
this
a
rhombus???
 All four sides are congruent (the same)
Diagonals are perpendicular (form 90  angles)
Diagonals BISECT each  corner angle
A
B
60
D
30
C
Why
is
this
a
rhombus???
The third triangle angle MUST be 90 (180 - 60 - 30 = 90)

ANSWER:
Diagonals are perpendicular (form 90  angles)
A
B
60
D
30
C
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