Chapter 6.2 and 6.3

Parallelograms and Tests for Parallelograms

ParallelogramO A parallelogram is a quadrilateral

with both pairs of opposite sides parallel

Concept 1

Use Properties of Parallelograms

A. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find AD.

Use Properties of Parallelograms

B. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mC.

Use Properties of Parallelograms

C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mD.

A. 10

B. 20

C. 30

D. 50

A. ABCD is a parallelogram. Find AB.

A. 36

B. 54

C. 144

D. 154

B. ABCD is a parallelogram. Find mC.

A. 36

B. 54

C. 144

D. 154

C. ABCD is a parallelogram. Find mD.

Concept 3

Use Properties of Parallelograms and Algebra

A. If WXYZ is a parallelogram, find the value of r.

Use Properties of Parallelograms and Algebra

B. If WXYZ is a parallelogram, find the value of s.

Use Properties of Parallelograms and Algebra

C. If WXYZ is a parallelogram, find the value of t.

A. 2

B. 3

C. 5

D. 7

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

A. 4

B. 8

C. 10

D. 11

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

A. 4

B. 5

C. 6

D. 7

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

Parallelograms and Coordinate GeometryWhat 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

What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with verticesL(0, –3), M(–2, 1), N(1, 5), O(3, 1)?

A.

B.

C.

D.

Concept 1

Identify Parallelograms

Determine whether the quadrilateral is a parallelogram. Justify your answer.

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 .

Which method would prove 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.

A. m = 2

B. m = 3

C. m = 6

D. m = 8

Find m so that the quadrilateral is a parallelogram.

Concept 3

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.

A. yes

B. no

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.