Download Parallelogram Theorems

Section 8.6
Identify Special
Quadrilaterals
Quadrilaterals
A polygon with four sides.
Parallelograms
A quadrilateral with both
pairs of opposite sides
parallel and congruent.
Rhombus
Rectangle
A parallelogram
with 4 congruent
sides.
Square
A parallelogram
with 4 congruent
sides and 4 right
angles.
A parallelogram
with 4 right angles.
Kites
A quadrilateral
with 2 pairs of
adjacent sides
congruent and
no opposite sides
congruent.
Trapezoids
A quadrilateral with
exactly 1 pair of parallel
sides.
Isosceles
Trapezoid
A trapezoid
whose 2 nonparallel sides are
congruent.
Right
Trapezoid
A trapezoid
with exactly 2
right angles.
Parallelogram Theorems:
•Thm. 8.3: If a quadrilateral is a parallelogram, then its opposite SIDES are
congruent.
•Thm. 8.4: If a quadrilateral is a parallelogram, then its opposite ANGLES are
congruent.
•Thm. 8. 5: If a quadrilateral is a parallelogram, then its consecutive angles are
SUPPLEMENTARY.
•Thm. 8.6: If a quadrilateral is a parallelogram, then its diagonals bisect each
other.
Rhombus Theorems:
•Thm. 8.11 A parallelogram is a rhombus if and only if its diagonals
are perpendicular.
•Thm. 8.12 A parallelogram is a rhombus if and only if each diagonal
bisects a pair of opposite angles..
Rectangle Theorems:
•Thm. 8.13 A parallelogram is a rectangle if and only if its diagonals
are congruent.
•REMEMBER:* The theorems that apply to parallelograms,
ALSO apply to the special types of parallelograms –
rhombus, rectangle and square.
Kite Theorems:
•Thm. 8.18 If a quadrilateral is a kite, then its diagonals
are perpendicular.
•Thm. 8.19 If a quadrilateral is a kite, then exactly one pair of
of opposite angles are congruent.
REMEMBER: If it’s true for
parallelograms, it’s true for ALL
three types as well!
Use the theorems and definitions
of the quadrilaterals!
X
X
X
X
X
X
X
Right Trapezoid because it
has one pair of || sides.
Homework
Section 8-6
Pg. 554 – 556
3 – 11, 14 – 16,
33 – 35,
43, 44, 47 – 50
Geometry – Classifying Quadrilaterals
Quadrilaterals
P
R
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o
a
m
b
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s
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g
r
a
m
s
A polygon with four sides.
A quadrilateral with both
pairs of opposite sides
parallel and congruent.
Rectangle
A parallelogram
with 4 right angles.
A parallelogram
with 4 congruent
sides.
Square
A parallelogram with
4 congruent sides
and 4 right angles.
Kites
Trapezoids
A quadrilateral with
2 pairs of adjacent
sides congruent and
no opposite sides
congruent.
A quadrilateral with
exactly 1 pair of parallel
sides.
Isosceles
Trapezoid
A trapezoid whose
2 non-parallel
sides are
congruent.
Right
Trapezoid
A trapezoid with
exactly 2 right
angles.