6.4-6.6 Special Parallelograms, trapezoids, and kites

If ____________________________________, then a parallelogram is a square.

1) The diagonals are congruent 2) one angle is a right angle (definition)

Properties of an Isosceles Trapezoid

1) The nonparallel sides (legs) are congruent 2) The diagonals are congruent 3) The consecutive base angles are congruent

If _______________________________________, then a parallelogram is a rhombus.

1) the diagonals are perpendicular 2) one diagonal bisects at least one pair of opposite angles 3) all 4 sides are congruent (definition)

Properties of a rhombus

1. ALL parallelogram properties apply 2. All Sides are congruent 3. Diagonals are perpendicular 4. Diagonals bisect angles

Properties of a rectangle

1. All properties of a parallelogram 2. All angles are right 3. Diagonals are congruent

Properties of a square

1. All properties of a parallelogram 2. All properties of a rectangle (right angles, diagonals congruent) 3. All properties of a rhombus (diagonals perpendicular, all sides congruent, diagonals bisect the angles)

Properties of a kite

1. The diagonals are perpendicular. 3. 2 sets of congruent sides; Short sides congruent and long sides congruent 4. Exactly 1 pair of congruent angles 5. Non-Congruent angles bisected by diagonal

Definition of a rhombus

A parallelogram with four congruent sides

Definition of a square

A parallelogram with four congruent sides and four right angles.

Definition of a rectangle

A parallelogram with four right angles

Definition of a trapezoid

A quadrilateral with exactly one pair of parallel sides

Definition of a Kite

A quadrilateral with two pairs of adjacent, congruent sides and opposite sides not congruent

If a parallelogram is a rhombus, then its diagonals are _________________________________

Perpendicular

Length of a midsegment of a trapezoid

The average of the bases: (b1 + b2) / 2

midsegment of a trapezoid

a segment that connects the midpoints of the legs of a trapezoid

Definition of an Isosceles Trapezoid

a trapezoid with congruent legs

If a parallelogram is a rhombus, then each diagonal ___________________________________________________________________________

bisects a pair of opposite angles

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

congruent