Parallelograms have Properties

http://dg044.k12.sd.us/Ms. Goodhope’s PPT Adapted by Mrs. Radigan

What is a parallelogram?

A parallelogram is a quadrilateral with both pairs

of opposite sides parallel.

Properties of Every Parallelogram:

Both pairs of opposite sides are congruent.

Both pairs of opposite angles are congruent.

Consecutive angles are supplementary.

Diagonals bisect each other.

1) Which is a property of a parallelogram?

A) The diagonals are parallel. B) The diagonals are congruent. C) The diagonals bisect opposite

angles. D) The diagonals bisect each other.

2) Which is a property of a parallelogram?

A) Opposite angles are parallel. B) Opposite angles are congruent. C) The diagonals bisect opposite

angles. D) One pair of opposite sides are

parallel.

2) Which is NOT a property of a parallelogram?

A) Opposite angles are supplementary.

B) Opposite angles are congruent. C) The diagonals bisect each other. D) Opposite sides are congruent.

3) Which is a property of a parallelogram?

A). Opposite angles are supplementary.

B) Consecutive angles are supplementary.

C) The diagonals are congruent. D) Opposite sides are perpendicular.

4) Which is NOT a property of a parallelogram?

A). Opposite angles are congruent. B) Consecutive angles are

complementary. C) The diagonals bisect each other. D) Opposite sides are parallel.

“Special Parallelograms”

Rectangle Rhombus

Square

Quadrilaterals

Parallelogram

Rectangle

Rhombus

Square

What is a rectangle?

A rectangle is a parallelogram with four right angles.

What are the properties of a rectangle? All the properties of every

parallelogram. (What are these properties?)

And…….. All four angles are right angles. The diagonals are congruent.

Both pairs of opposite sides are congruent.

Both pairs of opposite angles are congruent.Consecutive adjacent

angles are supplementary.Diagonals bisect each other.

5)Which is a property of a rectangle?

A) Diagonals are perpendicular. B) All sides are congruent. C) Diagonals are congruent. D) Diagonals bisect opposite

angles.

6) Which is a property of a rectangle?

A) Diagonals are perpendicular. B) All angles are congruent. C) Diagonals are congruent. D) All sides are congruent.

7) Which is NOT a property of a rectangle?

A) Diagonals are congruent. B) All angles are congruent. C) Diagonals are congruent. D) All sides are congruent.

8) Which is NOT a property of a rectangle?

A) Diagonals bisect each other. B) Opposite angles are congruent. C) Diagonals bisect opposite

angles. D) Opposite sides are congruent.

What is a rhombus?

A rhombus is a parallelogram with four congruent sides.

What are the properties of a rhombus? All the properties of every

parallelogram. (What are these properties?)

AND….. The diagonals are perpendicular. Each diagonal bisects opposite

angles of the rhombus.

Both pairs of opposite sides are congruent.Both pairs of opposite angles are congruent.

Consecutive adjacent angles are supplementary.Diagonals bisect each other.

9) Which is the property of a rhombus?

A) The diagonals are congruent. B) The diagonals bisect opposite

angles. C) All angles are congruent. D) The sides are perpendicular.

10) Which is the property of a rhombus?

A) The diagonals are congruent. B) The diagonals bisect opposite

sides. C) All angles are congruent. D) The diagonals are

perpendicular.

11) Which is NOT the property of a rhombus?

A) Opposite sides are congruent. B) The diagonals bisect opposite

angles. C) Diagonals are congruent. D) The diagonals are

perpendicular.

12) Which is NOT the property of a rhombus?

A) Opposite sides are parallel. B) The diagonals are congruent. C) Diagonals are bisect each other. D) The diagonals are

perpendicular.

What is a square?

A square is a parallelogram with four right angles and four

congruent sides.

What are the properties of a square? A square has all the properties of

every parallelogram. A square has all the properties of a

rectangle. A square has all the properties of a

rhombus. A square is a parallelogram, a

rectangle, and a rhombus!

Both pairs of opposite sides are congruent.

Both pairs of opposite angles are congruent.Consecutive adjacent

angles are supplementary.Diagonals bisect each other.

13) How many properties does the square have?? A) 4 B) 8 C) 12 D) 24

Properties of a Square 1) Opposite sides are

congruent. 2) Opposite angles are

congruent. 3) Diagonals bisect each

other. 4) The diagonal cuts it

into two congruent triangles.

5) Diagonals are congruent.

6) Diagonals are perpendicular.

7) Diagonals bisect opposite angles.

8) All angles are congruent.

9) Consecutive angles are perpendicular.

10) Opposite sides are parallel.

11) All sides are congruent.

12) There are four sides.

14) All rectangles are squares.

True False

15) All squares are rectangles.

True False

16) All squares are rhombi.

True False

17) All rhombi are squares.

True False

When a person is referred to as a square it means that they are…

A) Cool B) Mean

C) Old Fashioned

D) Dumb

Summary Slide What is a parallelogram? Properties of Every Parallelogram: What is a rectangle? What are the properties of a rectangle? What is a rhombus? What are the properties of a rhombus? What is a square? What are the properties of a square?

Your turn:

1. Do: On your paper, list the properties of a square.

2. Think: How can you use these properties to determine the measures of sides, angles, and diagonals of a parallelogram? Be ready to share your thoughts!

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