6-2 Parallelograms You classified polygons with four sides as quadrilaterals. Recognize and apply properties of the sides and angles of parallelograms.

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6-2 Properties of Parallelograms page 294

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Presentation transcript:

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 Draw diagonals in your parallelogram. Measure the sides. Measure the diagonals. Measure the diagonal parts. Measure the angles.

Page 403

Page 404

A. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches A. CONSTRUCTION In suppose mB = 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 mB = 32, CD = 80 inches, BC = 15 inches B. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mC. mC + mB = 180 Cons. s in a are supplementary. mC + 32 = 180 Substitution mC = 148 Subtract 32 from each side. Answer: mC = 148

C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mD. mD = mB Opp. s of a are . = 32 Substitution Answer: mD = 32

A. ABCD is a parallelogram. Find AB.

B. ABCD is a parallelogram. Find mC.

C. ABCD is a parallelogram. Find mD.

Page 405

Find the following in parallelogram MNOP 15 M N 135° Q 45° 7 45° 135° P O d. MP = e. OP = f. MQ = g. NQ = NP = 21 MO = 11 7 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 Substitution Divide 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 bisect each other. s = 3 Subtract 7s from each side. Answer: s = 3

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

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,