Topic 8 Review: Parallelograms and their properties (ADD PICTURES)

Properties of Parallelograms

• opposite sides are congruent

• Opposite sides are parallel

• Adjacent angles are supplementary

• The diagonals bisect each other

• Two diagonals each divide the parallelogram into two congruent triangles

Properties of a rectangle

• all properties of a parallelogram

• 4 right angles

properties of a rhombus

• all properties of a parallelogram

• 4 congruent sides

• Perpendicular diagonals

• Diagonals bisect angles

Properties of a square

• all properties of a parallelogram, rectangle, and rhombus

• 4 right angles

• 4 congruent sides

• Perpendicular diagonals

• Diagonals bisect angles

Properties of a trapezoid

• one, and only one pair of sides is parallel

Properties of an isosceles trapezoid

• one, and only one pair of sides are parallel

• Les are congruent (non parallel sides)

• Base angles are congruent (2 sets)

• Opposite angles are supplementary

• Diagonals are congruent

What’s needed to classify/prove a trapezoid

One pair of parallel sides

What’s needed to classify/prove a parallelogram

Any one of the following

-two pairs of opposite sides parallel or congruent

-two pairs of opposite angles congruent

-consecutive angles are supplementary

-diagonals that Mideast each other

-one pair of sides congruent and parallel

What’s needed to classify/prove a rectangle

Any one property front he parallelogram list, plus one of the following:

-one right angle

-diagonals are congruent

What’s needed to prove/classify a rhombus:

Any one property from the parallelogram list, plus one of the following:

-diagonals are perpendicular

-one pair of consecutive sides is congruent

-a diagonal bisects one of the angles

What’s needed to classify/prove a square

Any one properly from the parallelogram list,

PLUS any one property from the rectangle list

PLUS any one property from the rhombus list

What happens when two diagonals bisect each other

The 4 segments created by the midpoint creates 2 pairs of congruent segments