1. Parallelograms and Tests for Parallelograms
Chapter 6.2 and 6.3
Parallelograms and
Tests for Parallelograms

2. Parallelogram
A parallelogram is a quadrilateral with both pairs of opposite sides parallel

3. Concept 1

4. Use Properties of Parallelograms
A. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find AD.

5. Use Properties of Parallelograms
B. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mC.

6. Use Properties of Parallelograms
C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mD.

7. A. ABCD is a parallelogram. Find AB.

8. B. ABCD is a parallelogram. Find mC.

9. C. ABCD is a parallelogram. Find mD.

10. Concept 3

11. A. If WXYZ is a parallelogram, find the value of r.
Use Properties of Parallelograms and Algebra
A. If WXYZ is a parallelogram, find the value of r.

12. B. If WXYZ is a parallelogram, find the value of s.
Use Properties of Parallelograms and Algebra
B. If WXYZ is a parallelogram, find the value of s.

13. C. If WXYZ is a parallelogram, find the value of t.
Use Properties of Parallelograms and Algebra
C. If WXYZ is a parallelogram, find the value of t.

14. A. If ABCD is a parallelogram, find the value of x.

15. B. If ABCD is a parallelogram, find the value of p.

16. C. If ABCD is a parallelogram, find the value of k.

17. Parallelograms and Coordinate Geometry
What are the coordinates of the intersection of the diagonals of parallelogram MNPR, with vertices M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)?
Since the diagonals of a parallelogram bisect each other, the intersection point is the midpoint of

18. What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with vertices L(0, –3), M(–2, 1), N(1, 5), O(3, 1)? A. B. C. D.

19. Concept 1

20. Identify Parallelograms
Determine whether the quadrilateral is a parallelogram. Justify your answer.

21. 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 .

22. 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.

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

24. Concept 3

25. COORDINATE GEOMETRY Quadrilateral QRST has vertices
Parallelograms and Coordinate Geometry
COORDINATE GEOMETRY Quadrilateral QRST has vertices
Q(–1, 3), R(3, 1), S(2, –3), and T(–2, –1). Determine whether the quadrilateral is a parallelogram. Justify your answer by using the Slope Formula.
If the opposite sides of a quadrilateral are parallel, then it is a parallelogram.

26. Graph quadrilateral EFGH with vertices E(–2, 2), F(2, 0), G(1, –5), and H(–3, –2). Determine whether the quadrilateral is a parallelogram using the distance formula and slope formula.
A. yes
B. no