Lesson 6-3: Rectangles 1

Lesson 6-3

Rectangles

Lesson 6-3: Rectangles 2

Rectangles

Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other.

Definition: A rectangle is a parallelogram with four right angles.

A rectangle is a special type of parallelogram. Thus a rectangle has all the properties of a parallelogram.

Lesson 6-3: Rectangles 3

Properties of Rectangles

Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles.

If a parallelogram is a rectangle, then its diagonals are congruent.

E

D C

BA

Theorem:

Converse: If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle.

Lesson 6-3: Rectangles 4

Examples…….

1. If AE = 3x +2 and BE = 29, find the value of x.

2. If AC = 21, then BE = _______.

3. If m<1 = 4x and m<4 = 2x, find the value of x.

4. If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6.

m<1=50, m<3=40, m<4=80, m<5=100, m<6=40

10.5 units

x = 7 units

x = 18 units

6

54

321

E

D C

BA