6-2 Parallelograms

You classified polygons with four sides as quadrilaterals.

• Recognize and apply properties of the sides and angles of parallelograms.

• Recognize and apply properties of the diagonals of parallelograms.

Parallelogram Probe

1. Draw diagonals in your parallelogram.

2. Measure the sides.

3. Measure the diagonals.

4. Measure the diagonal parts.

5. Measure the angles.

Page 403

Page 404

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

AD = BC Opposite sides of a are .

= 15 Substitution

Answer: AD = 15 inches

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

Answer: mC = 148

mC + mB = 180 Cons. s in a are supplementary.

mC + 32 = 180 Substitution

mC = 148 Subtract 32 from each side.

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

Answer: mD = 32

mD = mB Opp. s of a are .

= 32 Substitution

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.

Page 405

Find the following in parallelogram MNOP

d. MP =

e. OP =

f. MQ =

g. NQ =

PMNm.a

MNOmc.OPMmb.

M N

OP

Q

135°

7

15

NP = 21

MO = 11

135°

45°

7

45°

15

5.5

10.5

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

Opposite sides of a parallelogram are .Definition of congruence

SubstitutionDivide each side by 4.

Answer: r = 4.5

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

8s = 7s + 3 Diagonals of a bisecteach other.

Answer: s = 3

s = 3 Subtract 7s from each side.

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.

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

Find the midpoint of

Midpoint Formula

Answer: The coordinates of the intersection of the diagonals of parallelogram MNPR are (1, 2).

Properties of Parallelograms• The opposite sides of a parallelogram are

parallel (by definition).• The opposite angles of a parallelogram are

congruent.• The opposite sides of a parallelogram are

congruent.• The consecutive angles of a parallelogram

are supplementary.• The diagonals of a parallelogram bisect each

other

• What is true about the opposite sides of a parallelogram?

They are parallel and congruent.

• What is true about the opposite angles?

They are congruent.

• What is true about the consecutive angles?

They are supplementary.

• What is true about the diagonals?

They bisect each other.

6-2 Assignment

• Page 407, 9-12,