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Lesson 6-3
Tests for Parallelograms
5-Minute Check on Lesson 6-2
Complete each statement about parallelogram ABCD
A
B
1. AB  ______
2. AD  ______
D
C
3. D  ______
In the figure RSTU is a parallelogram
Find the indicated value.
4.
x
6.
5.
y
6(x+5)
S
(12y+19)°
R
(8y+1)°
T
12x+6
U
Standardized Test Practice: Which congruence statement is not
necessarily true, if WXYZ is a parallelogram?
WX  YZ
A
WZ  XZ
B
C
W  Y
D
X  Z
Click the mouse button or press the
Space Bar to display the answers.
X
W
Z
Y
5-Minute Check on Lesson 6-2
Complete each statement about parallelogram ABCD
A
DC
1. AB  ______
Opposite sides are congruent
BC
2. AD  ______
Opposite sides are congruent
D
3. D  ______
Opposite angles are congruent
In the figure RSTU is a parallelogram
Find the indicated value.
4.
x
6.
5.
4
y
D
C
6(x+5)
S
(12y+19)°
R
8
B
(8y+1)°
T
12x+6
U
Standardized Test Practice: Which congruence statement is not
necessarily true, if WXYZ is a parallelogram?
WX  YZ
A
WZ  XZ
B
C
W  Y
D
X  Z
Click the mouse button or press the
Space Bar to display the answers.
X
W
Z
Y
Objectives
• Recognize the conditions that ensure a
quadrilateral is a parallelogram
– A quadrilateral is a parallelogram if any of the
following is true:
•
•
•
•
•
Both pairs of opposite sides are parallel
Both pairs of opposite sides are congruent
Both pairs of opposite angles are congruent
Diagonals bisect each other
A pair of opposite sides is both parallel and congruent
• Prove that a set of points forms a
parallelogram in the coordinate plane
Vocabulary
• None new
Tests for Parallelograms
A
B
M
Quadrilateral is a Parallelogram
(if any of the following are true):
C
a) Both Pairs of Opposite Sides Are Parallel
b) Both Pairs of Opposite Sides Are Congruent
c) A Pair of Opposite Sides Is Both Parallel and Congruent
d) Both Pairs of Opposite Angles Are Congruent
e) Diagonals Bisect Each Other
D
Determine whether the quadrilateral is a parallelogram.
Justify your answer.
Answer: Each pair of opposite sides have the same
measure. Therefore, they are congruent. If both
pairs of opposite sides of a quadrilateral are
congruent, the quadrilateral is a parallelogram.
Determine whether the quadrilateral is a parallelogram.
Justify your answer.
Answer: One pair of opposite sides is parallel and has
the same measure, which means these sides
are congruent. If one pair of opposite sides of a
quadrilateral is both parallel and congruent,
then the quadrilateral is a parallelogram.
Find x so that the quadrilateral is a parallelogram.
A
B
Opposite sides of a
parallelogram are congruent.
D
C
Substitution
Distributive Property
Subtract 3x from each side.
Add 1 to each side.
Answer: When x is 7, ABCD is a parallelogram.
Find y so that the quadrilateral is a parallelogram.
D
E
Opposite angles of a
parallelogram are congruent.
G
F
Substitution
Subtract 6y from each side.
Subtract 28 from each side.
Divide each side by –1.
Answer: DEFG is a parallelogram when y is 14.
Find m and n so that each quadrilateral is a parallelogram.
a.
Answer:
b.
Answer:
Ch 6 Quiz 1 Need to Know
• Angles in Convex Polygons (n = # of sides)
–
–
–
–
Interior angle + Exterior angle = 180°
Sum of Interior angles = (n-2) 180°
Sum of Exterior angles = 360°
Shortcut for sides (360° / exterior angle) = n
• Parallelogram Characteristics
–
–
–
–
Opposite sides parallel and congruent ()
Opposite angles congruent ()
Consecutive angles supplementary (add to 180°)
Diagonals bisect each other
Summary & Homework
• Summary:
– A quadrilateral is a parallelogram if any of
the following is true:
• Both pairs of opposite sides are parallel and
congruent
• Both pairs of opposite angles are congruent
• Diagonals bisect each other
• A pair of opposite sides is both parallel and
congruent
• Homework:
– pg 413-15; 1, 2, 4-5, 9-14, 19, 20