1. Lesson 6-1: Parallelogram
Definition:
A quadrilateral whose opposite sides are parallel. C B A D
Symbol:
a smaller version
of a parallelogram
Naming:
A parallelogram is named using all four vertices.
You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction.
For example, the figure above can be either ABCD or ADCB.
Lesson 6-1: Parallelogram

2. Rectangles 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.
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.
Lesson 6-3: Rectangles

3. Properties of Rectangles
Theorem:
If a parallelogram is a rectangle, then its diagonals are congruent.
Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles. E D C B A
Converse:
If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle.
Lesson 6-3: Rectangles

4. Lesson 6-4: Rhombus & Square
Definition:
A rhombus is a parallelogram with four congruent sides. ≡ ≡
Since a rhombus is a parallelogram the following are true:
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other
Lesson 6-4: Rhombus & Square

5. Properties of a Rhombus
Theorem:
The diagonals of a rhombus are perpendicular.
Theorem:
Each diagonal of a rhombus bisects a pair of opposite angles.
Lesson 6-4: Rhombus & Square

6. Lesson 6-4: Rhombus & Square
Definition:
A square is a parallelogram with four congruent angles and four congruent sides.
Since every square is a parallelogram as well as a rhombus and rectangle, it has all the properties of these quadrilaterals.
Opposite sides are parallel.
Four right angles.
Four congruent sides.
Consecutive angles are supplementary.
Diagonals are congruent.
Diagonals bisect each other.
Diagonals are perpendicular.
Each diagonal bisects a pair of opposite angles.
Lesson 6-4: Rhombus & Square

7. Lesson 6-5: Trapezoid & Kites
Definition:
A quadrilateral with exactly one pair of parallel sides.
The parallel sides are called bases and the non-parallel sides are called legs.
Trapezoid
Base
Leg
An Isosceles trapezoid is a trapezoid with congruent legs.
Isosceles trapezoid
Lesson 6-5: Trapezoid & Kites

8. Properties of Isosceles Trapezoid
1. Both pairs of base angles of an isosceles trapezoid are congruent.
2. The diagonals of an isosceles trapezoid are congruent. B A
Base Angles D C
Lesson 6-5: Trapezoid & Kites

9. Lesson 6-1: Parallelogram
Kites
A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent.
**Diagonals are
perpendicular**
Lesson 6-1: Parallelogram