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Objectives: To define and classify special types of
quadrilaterals
 Definitions -> Special Quadrilaterals
 Parallelogram -> a quadrilateral with both pairs of

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



opposite sides parallel
Rhombus -> a parallelogram with four congruent sides
Rectangle -> a parallelogram with four right angles
Square -> a parallelogram with four congruent sides and
four right angles
Kite -> a quadrilateral with two pairs of adjacent sides
congruent and no opposite sides congruent
Trapezoid -> a quadrilateral with exactly one pair of
parallel sides
Isosceles Trapezoid -> a trapezoid whose nonparallel
opposite sides are congruent
 Ex: Classifying a Quadrilateral
 Classify the following figures in as many ways as possible
 Ex: Using the Properties of Special Quadrilaterals
 Find the values of the variable for the kite
T
2y + 5
x+6
J
K
2x + 4
3x - 5
B
 Ex:
 Find the values of the variables for the rhombus. Then
find the lengths of each side.
3b + 2
L
N
5a + 4
S
3a + 8
4b - 2
T
Homework #31
Due Tuesday (December 04)
Page 308 – 309
# 1 – 12 all
# 13 – 25 all
Section 6.2
Properties of Parallelograms
 Objectives: To use relationships among sides and
among angles of parallelograms
To use relationships involving diagonals of
parallelograms or transversals
 Theorem 6.1
 Opposite sides of a parallelogram are congruent
 Consecutive Angles -> angles of a polygon that share a
side. Since a parallelogram has opposite sides parallel,
consecutive angles are same-side interior angles
(supplementary)
D
A
C
B
<A and <B
<B and <C
<C and <D
<D and <A
 Ex: Using Consecutive Angles
 Find the measure of each missing angle in parallelogram
RSTW
S
T
112°
R
W
 Theorem 6.2
 Opposite angles of a parallelogram are congruent
 Ex:
 Find the value of x and y in parallelogram PQRS. Then
find the measures of each side and each angle.
Q
3x - 15
R
(3y + 37)°
P
(6y + 4)°
2x + 3
S
 Theorem 6.3
 The diagonals of a parallelogram bisect each other
JH congruent LH
KH congruent MH
J
K
H
M
L
 Ex:
 Find the value of x and y. Then find the value of each
line segment
B
C
E
A
D
 Theorem 6.4
 If three (or more) parallel lines cut off congruent
segments on one transversal, then they cut off
congruent segments on every transversal.
A
C
E
B
D
F
Homework #32
Due Wednesday (Dec 05)
Page 315 – 316
# 1 – 13 all
# 14 – 30 even
Section 6.3 - Proving that a
Quadrilateral is a Parallelogram
 Objectives: To determine whether a quadrilateral is a
parallelogram
 Theorem 6.5
 If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is a parallelogram
Since both pairs of opposite sides are congruent,
the above quadrilateral is also a parallelogram.
 Theorem 6.6
 If both pairs of opposite angles of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.
Since both pairs of opposite angles are congruent, the
above quadrilateral is also a parallelogram.
 Theorem 6.7
 If the diagonals of a quadrilateral bisect each other,
then the quadrilateral is a parallelogram.
Since the diagonals are bisected, the above
quadrilateral is also a parallelogram.
 Theorem 6.8
 If one pair of opposite sides of a quadrilateral is both
congruent and parallel, then the quadrilateral is a
parallelogram.
Since one pair of opposite sides are parallel and
congruent, the above quadrilateral is also a parallelogram.
 Ex: Finding Values for Parallelograms
 For what values of x and c must MLPN be a
parallelogram?
P
L
3c - 3
c+1
M
N
Homework #33
Due Thursday (Dec 06)
Page 324 – 325
# 1 – 19 all
Section 6.4
Special Parallelograms
 Objectives: To use properties of diagonals of
rhombuses and rectangles
To determine whether a parallelogram is a
rhombus or a rectangle
 Theorem 6.9
 Each diagonal of a rhombus bisects two angles of the
rhombus
B
3
1
A
C
4
< 1 congruent < 2
< 3 congruent < 4
2
D
 Theorem 6.10
 The diagonals of a rhombus are perpendicular
C
B
AC perpendicular BD
A
D
 Theorem 6.11
 The diagonals of a rectangle are congruent
A
D
AC congruent BD
B
C
 Theorem 6.12
 If one diagonal of a parallelogram bisects two angles of
the parallelogram, then the parallelogram is a rhombus.
 Theorem 6.13
 If the diagonals of a parallelogram are perpendicular,
then the parallelogram is a rhombus.
 Theorem 6.14
 If the diagonals of a parallelogram are congruent, then
the parallelogram is a rectangle.
Homework # 34
Due Monday (December 10)
Page 332 – 334
# 1 – 17 odd
# 41 – 46 all
Section 6.5
Trapezoids and Kites
 Objectives: To verify and use properties of trapezoids
and kites
 Base Angles -> two angles that share a base of a
trapezoid. Since the bases of the trapezoid
are parallel, the two angles that share a leg
are supplementary.
Base Angles
Leg
Leg
Base Angles
 Theorem 6.15
 The base angles of an isosceles trapezoid are congruent
 Ex:
 Find the measure of each angle in the following
trapezoid
B
C
P
Q
102°
70°
S
A
D
R
 Theorem 6.16
 The diagonals of an isosceles trapezoid are congruent
 Theorem 6.17
 The diagonals of a kite are perpendicular
 Ex:
 Find the measures of < 1, < 2, and < 3 in the kite
B
3
A
32°
1
D
2
C
Homework # 35
Due Monday (December 10)
Page 338 – 340
# 1 – 27 odd
Quiz Tuesday (Dec 11)
Chapter 6 Test Thursday/Friday