ParallelogramsUnit 9, Lesson 2 & 3

By definition, a parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Parallelograms have:◦ 2 sets of parallel sides◦ 2 sets of congruent sides◦ opposite angles congruent◦ consecutive angles supplementary◦ diagonals bisect each other◦ diagonals form 2 congruent triangles

What is a parallelogram?

Complete each statement about parallelogram QRST.

Justify your answer.

A.

B.

C. ∠TSR is supplementary to _____.

Example #1

_____SV

_____VRS

Use parallelogram JKLM to find each measure or value.

A. m∠MJK = _____

B. m∠JML = _____

C. m∠JKL = _____

D. m∠KJL = _____

E. a = _____ F. b = _____

Example #2

Parallelogram GHJK has vertices G(-3, 4), H(1, 1), and J(3, -5). Which are possible coordinates for vertex K?

A. (-1, 1)

B. (-2, 0)

C. (-1, -2)

D. (-2, -1)

Example #3

The following quadrilaterals are parallelograms. Solve for x and y.

4. 5.

6.

x - 4

3y - 8

2x - 12

(y – 4) (3x + 3)

(x + 27)

3x - 63x – 1

6

x + 183y + 2

Given: Parallelogram ACDE;

Prove: E D

CBA

Parallelogram ACDE

Given Given

Opposite sides of a

parallelogram are congruent.

Transitive property

If two sides of a triangle are congruent, then the angles

opposite them are also congruent.

AE BD

CBD C

AE BD

AE CD

CD BD

CBD C

Given: Parallelogram ACDE;

Prove: ∆BDC is isoscelesE D

CBA

Given

Opposite angles of a parallelogram are congruent.

Parallelogram

ACDEGiven

Transitive property If 2 angles of a

triangle are congruent, then the sides opposite them are also congruent.

∆BDC is isosceles

Definition of isosceles triangle

CBD E

CBD E

E C

CBD C BD CD