Lesson 6-3

Test for Parallelograms

Identify Parallelograms

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

Answer: 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?

Use Parallelograms to Prove Relationships

MECHANICS Scissor lifts, like the platform lift shown, are commonly applied to tools intended to lift heavy items. In the diagram, A C and B D. Explain why the consecutive angles will always be supplementary, regardless of the height of the platform.

Use Parallelograms to Prove Relationships

Answer: Since both pairs of opposite angles of quadrilateral ABCD are congruent, ABCD is a parallelogram by Theorem 6.10. Theorem 6.5 states that consecutive angles of parallelograms are supplementary. Therefore, mA + mB = 180 and mC + mD = 180. By substitution, mA + mD = 180 and mC + mB = 180.

The diagram shows a car jack used to raise a car from the ground. In the diagram, AD BC and AB DC. Based on this information, which statement will be true, regardless of the height of the car jack.

A. A B

B. A C

C. AB BC

D. mA + mC = 180

Use Parallelograms and Algebra to Find Values

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

A. m = 2

B. m = 3

C. m = 6

D. m = 8

Find m so that the quadrilateral is a parallelogram.