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Section 5-4
Special
Parallelograms
RECTANGLE
•A rectangle is a quadrilateral
with four right angles.
Therefore, every rectangle is a
parallelogram.
Rectangle
• Why?
D
C
A
B
• Both pairs of opposite angles
are congruent.
Rhombus
•A rhombus is a quadrilateral
with four congruent sides.
Therefore, every rhombus is a
parallelogram.
rhombus
• Why?
D
A
C
B
• Both pairs of opposite sides
are congruent.
Square
•A square is a quadrilateral with
four right angles and four
congruent sides. Therefore,
every square is a rectangle, a
rhombus, and a parallelogram.
Square
• Why?
D
C
A
B
•Both pairs of opposite angles
(and sides) are congruent.
Conclusion:
Since rectangles,
rhombuses and squares
are all parallelograms,
they have all the
properties of a
parallelogram.
Theorem 5-12
•The diagonals of a rectangle
are congruent.
D
C
A
B
AC  DB
Theorem 5-13
•The diagonals of a rhombus
are perpendicular.
D
A
C
B
Theorem 5-14
•Each diagonal of a rhombus
bisects two angles of the
D
rhombus.
A
C
B
Theorem 5-15
•The midpoint of the hypotenuse
of a right triangle is equidistant
from the vertices.
A
D
B
C
Theorem 5-16
•If an angle of a parallelogram is
a right angle, then the
parallelogram is a rectangle.
D
C
Angle A is a Rt. Angle
Thus,
ABCD is a Rectangle!
A
B
Theorem 5-17
•If two consecutive sides of a
parallelogram are congruent,
then the parallelogram is a
rhombus.
Theorem 5-17
AB  BC
Thus, ABCD is a Rhombus
D
A
C
B
Always, Sometimes or Never?
• A square is _________
Always a rhombus?
• The diagonals of a parallelogram
____________
Sometimes bisect the angles of the
parallelogram?
• A quadrilateral with one pair of sides
congruent and one pair parallel is
___________
Sometimes a parallelogram?
Always, Sometimes or Never?
• The diagonals of a rhombus are
Sometimes
___________ congruent?
• A rectangle Sometimes
__________ has
consecutive sides congruent?
• A rectangle __________
Sometimes has
perpendicular diagonals?
Always, Sometimes or Never?
• The diagonals of a rhombus
Always
___________ bisect each other?
• The diagonals of a parallelogram
are __________
Sometimes perpendicular
bisectors of each other?