Classifying Quadrilaterals name removed Geometry December 8 2014

Classifying Quadrilaterals {name removed} Geometry December 8, 2014

The Rectangle • A rectangle is a four sided quadrilateral where every angle is a right angle. Opposite sides are parallel and equal length.

The Rhombus • A rhombus is a four-sided shape where all sides have equal length. Also opposite sided are parallel and opposite angles are congruent. The diagonals meet in the middle at a right angle.

The Square • A square has equal sides and every angle is a right angle, opposite sides are parallel. A square also fits the definition of a rectangle and a rhombus.

The Parallelogram • A parallelogram is a quadrilateral with two pairs of parallel sides, opposite angles are congruent.

The Isosceles Trapezoid • A quadrilateral with one pair of Parallel sides.

The Kite • A kite is a quadrilateral with 2 pairs of congruent sides where the sides are adjacent.

To Tell If a Quadrilateral is a Rectangle • By first showing it is a parallelogram. • If a parallelogram contains at least one right angle, then it is a rectangle by definition. • If the diagonals are congruent, then it is a rectangle. • If all the angles are of the parallelogram are right angles, then it is a rectangle.

To Tell If a Quadrilateral is a Rhombus • By first showing it is a parallelogram. • If a parallelogram has a pair of consecutive sides that are congruent, then it is a rhombus by definition. • If either diagonals bisects two angles of a parallelogram, then it is a rhombus. • If the diagonals are perpendicular bisectors of each other, than it is a rhombus.

To Tell If a Quadrilateral is a Square • If the quadrilateral is both a rectangle and a rhombus, then it is a square.

To Tell If a Quadrilateral is a Parallelogram • If to pairs of opposite side are parallel, then by definition its is a parallelogram. • If the two pairs of opposite sides are congruent, then it is a Parallelogram. • At least one pair of opposite sides are parallel and congruent. • If the diagonals bisect one another, then it is a parallelogram. • If the opposite angles are congruent, then it is a parallelogram. • If the diagonals bisect two angles

To Tell If a Quadrilateral is a Kite • If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it is a kite. • If one of the diagonals of a quadrilateral is the perpendicular bisector of the other diagonal, then it is a kite.

Example 1: • Give the most specific name for the following quadrilateral. • Explanation: the definition of a kite is a quadrilateral with 2 pairs of congruent sides where the sides are adjacent meaning that the congruent sides are next to one another. • Solution (to see what else to add go to The Kite slide) Start with what was given. What else needs to be added.

Example 2: • Give the most specific name for the following quadrilateral. • Explanation: The definition of a parallelogram is a quadrilateral with 2 pairs of parallel sides, opposite angles are congruent. • Solution: (to see what else to add go to The Parallelogram slide) Start with what was given, and add.

Give the most specific name for the following quadrilateral. 1. 2. 4. 3. 5.

Answers: • 1. Trapezoid • 2. Parallelogram • 3. Rectangle • 4. square • 5. Kite

Work Cited • Class Notes