1. Tests for Parallelograms
Lesson 8-3
Tests for Parallelograms

2. 5-Minute Check on Lesson 8-2
Complete each statement about parallelogram ABCD
1. AB  ______
2. AD  ______
3. D  ______
In the figure RSTU is a parallelogram Find the indicated value.
x y
Which congruence statement is not necessarily true, if WXYZ is a parallelogram?
Transparency 8-3
5-Minute Check on Lesson 8-2 A B C D
6(x+5) R S
(12y+19)°
(8y+1)° U T
12x+6
Standardized Test Practice: W X A
WZ  XZ B
WX  YZ Z Y C
W  Y D
X  Z
Click the mouse button or press the Space Bar to display the answers.

3. 5-Minute Check on Lesson 8-2
Complete each statement about parallelogram ABCD
1. AB  ______
2. AD  ______
3. D  ______
In the figure RSTU is a parallelogram Find the indicated value.
x y
Which congruence statement is not necessarily true, if WXYZ is a parallelogram?
Transparency 8-3
5-Minute Check on Lesson 8-2 A B C D DC
Opposite sides are congruent BC
Opposite sides are congruent D
Opposite angles are congruent
6(x+5) R S
(12y+19)°
(8y+1)° 4 8 U T
12x+6
Standardized Test Practice: W X A
WZ  XZ B
WX  YZ Y C
W  Y Z D
X  Z
Click the mouse button or press the Space Bar to display the answers.

4. 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

5. Vocabulary
None new

6. 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
e) Diagonals Bisect Each Other A B M C D

7. Determine whether the quadrilateral is a parallelogram
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.
Example 3-3a

8. Determine whether 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.
Example 3-3b

9. Find x so that the quadrilateral is a parallelogram.B C D
Opposite sides of a parallelogram are congruent.
Substitution
Distributive Property
Subtract 3x from each side.
Add 1 to each side.
Answer: When x is 7, ABCD is a parallelogram.
Example 3-4a

10. Find y so that the quadrilateral is a parallelogram.
Opposite angles of a parallelogram are congruent.
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.
Example 3-4c

11. Find m and n so that each quadrilateral is a parallelogram.b.
Answer:
Answer:
Example 3-4e

12. 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

13. Summary & Homework Summary: Homework:
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 ; , 26-27, 45-46