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

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

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

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

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

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

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

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

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