6-3 Tests for Parallelograms

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.

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.

Write the Converse of the definition

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

A quadrilateral is a parallelogram if both pairs of opposite sides are parallel (definition).

1. Draw a parallelogram on a piece of graph paper.

2. How do you check for 2 pairs of parallel sides?

Write the converse of:The opposite angles of a parallelogram are congruent.

If both pairs of angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

1. Measure the angles of your parallelogram.

Write the Converse of

The opposite sides of a parallelogram are congruent.

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

1. Measure the length of the sides of your quadrilateral. Write down the measurements.

Write the Converse of

The consecutive angles of a parallelogram are supplementary.

If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.

1. Add up the measures of the consecutive angles. Are they supplementary?

Write the Converse ofThe diagonals of a parallelogram bisect each

other.

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

1. Draw diagonals in your quadrilateral.

2. Measure the diagonals.

3. Measure each part of the diagonals and write down the measurement.

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Is the quadrilateral a parallelogram?

Yes, Opposite sides are congruent.

Yes, consecutive angles are supplementary.

Yes, diagonals bisect each other.

?? The congruent sides may not be parallel.

70°110°

110°

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.

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?

Find x and y so that the quadrilateral is a parallelogram.

Opposite sides of a parallelogram are congruent.

Substitution

Distributive Property

Add 1 to each side.

Subtract 3x from each side.

AB = DC

Answer: So, when x = 7 and y = 5, quadrilateral ABCD is a parallelogram.

Substitution

Distributive Property

Add 2 to each side.

Subtract 3y from each side.

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.

Answer: Since opposite sides have the same slope, QR║ST and RS║TQ. Therefore, QRST is a parallelogram by definition.

Conditions for a Parallelogram• A quadrilateral is a parallelogram if both pairs of

opposite sides are parallel (definition).• If both pairs of angles of a quadrilateral are congruent,

then the quadrilateral is a parallelogram.• If both pairs of opposite sides of a quadrilateral are

congruent, then the quadrilateral is a parallelogram.

• If the consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram.

• If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

6-3 Assignment

Page 418, 9-14, 18-24

18-24 Show your work!

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