Transcript Document
Lesson 8-3
Tests for Parallelograms
5-Minute Check on Lesson 8-2 Transparency 8-3 Complete each statement about parallelogram ABCD 1. AB
______ 2. AD
______ 3.
D
______ D A In the figure RSTU is a parallelogram Find the indicated value.
R 6(x+5) (12y+19) ° S 4. x 5. y U C (8y+1) ° 12x+6 T B necessarily true, if WXYZ is a parallelogram?
A WZ
XZ B WX
YZ C
W
Y D
X
Z Click the mouse button or press the Space Bar to display the answers.
W Z X Y
5-Minute Check on Lesson 8-2 Transparency 8-3 Complete each statement about parallelogram ABCD 1. AB
Opposite sides are congruent
2. AD
3.
D
Opposite sides are congruent Opposite angles are congruent
D A In the figure RSTU is a parallelogram Find the indicated value.
R 6(x+5) (12y+19) ° S 8 U C (8y+1) ° 12x+6 T B necessarily true, if WXYZ is a parallelogram?
A WZ
XZ B WX
YZ C
W
Y D
X
Z Click the mouse button or press the Space Bar to display the answers.
W Z X Y
Objectives
•
Recognize the conditions that ensure a quadrilateral is a parallelogram
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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
•
None new
Vocabulary
Tests for Parallelograms
Quadrilateral is a Parallelogram (if any of the following are true): 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 A e) Diagonals Bisect Each Other M C D B
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 3
x
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 6
y
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.
b.
Answer: Answer:
Ch 8 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:
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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:
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pg 421-423; 15-22, 26-27, 45-46