1. Tests for Parallelograms
LESSON 6–3
Tests for Parallelograms

2. Five-Minute Check (over Lesson 6–2) TEKS Then/Now
Theorems: Conditions for Parallelograms
Proof: Theorem 6.9
Example 1: Identify Parallelograms
Example 2: Real-World Example: Use Parallelograms to Prove Relationships
Example 3: Use Parallelograms and Algebra to Find Values
Concept Summary: Prove that a Quadrilateral Is a Parallelogram
Example 4: Parallelograms and Coordinate Geometry
Example 5: Parallelograms and Coordinate Proofs
Lesson Menu

3. ____ ? A. B. C.
5-Minute Check 1

4. ? A. B. C.
5-Minute Check 2

5. ?
A. A
B. B
C. C
5-Minute Check 3

6. An expandable gate is made of parallelograms that have angles that change measure as the gate is adjusted. Which of the following statements is always true?
A. A  C and B  D
B. A  B and C  D C. D.
5-Minute Check 4

7. Mathematical Processes G.1(D), G.1(G)
Targeted TEKS
G.6(E) Prove a quadrilateral is a parallelogram, rectangle,
square, or rhombus using opposite sides, opposite angles, or diagonals and apply these relationships to solve problems.
Mathematical Processes
G.1(D), G.1(G)
TEKS

8. You recognized and applied properties of parallelograms.
Recognize the conditions that ensure a quadrilateral is a parallelogram.
Prove that a set of points forms a parallelogram in the coordinate plane.
Then/Now

9. Concept 1

10. Identify Parallelograms
Determine whether the quadrilateral is a parallelogram. Justify your answer.
Answer: Each pair of opposite sides has the same measure. Therefore, they are congruent. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram.
Example 1

11. Which method would prove the quadrilateral is a parallelogram?
A. Both pairs of opp. sides ||.
B. Both pairs of opp. sides .
C. Both pairs of opp. s .
D. One pair of opp. sides both || and .
Example 1

12. The diagram shows a car jack used to raise a car from the ground
The diagram shows a car jack used to raise a car from the ground. In the diagram, AD  BC and AB  DC. Based on this information, which statement will be true, regardless of the height of the car jack.
A. A  B
B. A  C
C. AB  BC
D. mA + mC = 180
Example 2

13. Find x and y so that the quadrilateral is a parallelogram.
Use Parallelograms and Algebra to Find Values
Find x and y so that the quadrilateral is a parallelogram.
Opposite sides of a parallelogram are congruent.
Example 3

14. Distributive Property
Use Parallelograms and Algebra to Find Values
AB = DC
Substitution
Distributive Property
Subtract 3x from each side.
Add 1 to each side.
Example 3

15. Distributive Property
Use Parallelograms and Algebra to Find Values
Substitution
Distributive Property
Subtract 3y from each side.
Add 2 to each side.
Answer: So, when x = 7 and y = 5, quadrilateral ABCD is a parallelogram.
Example 3

16. Find m so that the quadrilateral is a parallelogram.
B. m = 3
C. m = 6
D. m = 8
Example 3

17. Concept 3

18. Tests for Parallelograms
LESSON 6–3
Tests for Parallelograms