1. Parallelograms
Unit 9, Lesson 2 & 3

2. What is a parallelogram?
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

3. Example #1 Complete each statement about parallelogram QRST.
Justify your answer.
∠TSR is supplementary to _____.
segment VQ; diagonals of a parallelogram bisect each other
triangle VTQ; SSS (diagonals bisect each other and opposite sides of a parallelogram are congruent)
angle STQ and angle SRQ; consecutive angles of parallelogram are supplementary

4. Example #2 Use parallelogram JKLM to find each measure or value.
m∠MJK = _____
m∠JML = _____
m∠JKL = _____
m∠KJL = _____
E. a = _____ F. b = _____
100 80 30 7 21

5. Example #3 Parallelogram GHJK has vertices G(-3, 4),
H(1, 1), and J(3, -5). Which are possible coordinates for vertex K?
(-1, 1)
(-2, 0)
(-1, -2)
(-2, -1)
C is correct answer

6. The following quadrilaterals are parallelograms. Solve for x and y. 6.
x - 4
3y - 8
2x - 12
(y – 4)
(3x + 3)
(x + 27)
3x - 6
3x – 16
x + 18
3y + 2
x = 8, y = 4
x = 12; y = 145
x = 12; y = 6

7. Opposite sides of a parallelogram are congruent.B A
Given: Parallelogram ACDE;
Prove:
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.

8. Definition of isosceles triangleB A
Given: Parallelogram ACDE;
Prove: ∆BDC is isosceles
Parallelogram ACDE
Given
Given
Opposite angles of a parallelogram are congruent.
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