Rectangles

1
Rectangles
2
Goals

• Define rectangle. Discuss characteristics
  specific to rectangles.
• Determine whether parallelograms are rectangles.

3
Properties of a Parallelogram(Review)

• Definition Both pairs opp. sides of are
  parallel.
• Both pairs opp. sides are congruent
• Both pairs opp. angles are congruent
• All consecutive angles add to 180.
• Diagonals bisect each other.
• One pair of sides is parallel and congruent.

What are rectangles???
4
Rectangle - Definition

• A rectangle is a parallelogram where all 4 angles
  are congruent, each is 90.

The characteristics of parallelograms are also
true for rectangles, since it is a special type
of parallelogram.
5
Rectangle - Diagonals

• If a parallelogram is a rectangle, then the
  diagonals are congruent.

A
B
What is the relationship between AC and BD?
If ABCD is a rectangle, then
C
D
6
Rectangle - Diagonals

• If a parallelogram is a rectangle, then the
  diagonals are congruent.

A
B
C
D

• If the diagonals of a parallelogram are
  congruent, then it is a rectangle.

7
Properties of a Parallelogram

• Definition Both pairs opp. sides of are
  parallel.
• Both pairs opp. sides are congruent
• Both pairs opp. angles are congruent
• All consecutive angles add to 180.
• Diagonals bisect each other.
• One pair of sides is parallel and congruent.

Properties of a Rectangle

• See above
• Definition All four angles are congruent
• Diagonals are congruent.