If a parallelogram has an area of A square units, a base of b units and a height of h units, then A = bh. (Do example 1 p. 530)
The area of a region is the sum of the areas of all its non-overlapping parts. (Do example 3 p. 531)
A rectangle is a quadrilateral with four right angles.
Theorem 6-9 : If a parallelogram is a rectangle,
then its diagonals are congruent.
Opp. angles in rectangles are congruent (they are right angles) therefore rectangles are parallelograms with all their properties.
Theorem 6-10 : If the diagonals of a parallelogrma
are congruent then the parallelogram is a rectangle.
If a quadrilateral is a rectangle, then the following properties hold true:
Opp. Sides are congruent and parallel
Opp. Angles are congruent
Consecutive angles are supplementary
Diagonals are congruent and bisect each other
All four angles are right angles
A rhombus is a quadrilateral with four congruent sides. Since opp. sides are , a rhombus is a parallelogram with all its properties.
Special facts about rhombi
Theorem 6.11: The diagonals of a rhombus
Theorem 6.12: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
Theorem 6.13: Each diagonal of a rhombus bisects
a pair of opp. angles
Squares and Rhombi(2)
If a quadrilateral is both, a rhombus and a rectangle, is a square
If a rhombus has an area of A square units and diagonals of d1 and d2 units, then A = ½ d1d2.
If a triangle has an area of A square units a base of b units and corresponding height of h units, then A = ½bh.
Congruent figures have equal areas.
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
The parallel sides are called bases.
The nonparallel sides are called legs.
At each side of a base there is a pair of base angles.
AB = base
CD = base
AC = leg
BD = leg
AC & BD are non parallel
<A & <B = pair of base angles