Chapter 11

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Quadrilateral Properties: General

* the angles of a quadrilateral add up to 360 degrees

* a quadrilateral has four sides

Parallelogram:

* opposite sides are parallel and congruent

* opposite angles are congruent

* consecutive angles are supplementary

* diagonals bisect each other

Rhombus:

* all parallelogram properties

* all sides congruent (ALL ANGLES ARE NOT CONGRUENT)

* diagonals are perpendicular

* diagonals bisect opposite angles

Rectangle:

*all parallelogram properties

* all right angles

* diagonals are congruent

Square:

* all parallelogram properties

* all sides are congruent

* diagonals are perpendicular

* diagonals are congruent

* diagonals bisect opposite angles

Kite:

* two disjoint pairs of congruent sides

* longer diagonal is the perpendicular bisector of the shorter diagonal

* diagonals bisect opposite angles

* one set of opposite angles is congruent

Trapezoid:

* exactly one pair of parallel sides

* midsegment theorem: 1/2 (sum of bases)

Isosceles Trapezoid:

* exactly one pair of parallel sides

* legs are congruent

* base angles are congruent

* consecutive angles are supplementary

* consecutive angles are congruent

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10.1 Areas of parallelograms and triangles

Area of a parallelogram:

b*h or bh

multiply the base (any slanted side of the parallelogram, stick with the longer side) by the corresponding height. to find the height draw right triangles within the parallelogram.

Area of a triangle:

1/2bh

The triangle is half of a parallelogram or other related quadrilaterals, that is why the total area is multiplied by 1/2. The base is not the side opposite the right angle or the hypotenuse. Find an altitude within the triangle then calculate for area using the formula shown above.

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10.2 Area of Trapezoids, Rhombi, and Kites

Trapezoids:

A = 1/2h(b1+b2) OR A = (midsegment)(height)

the parallel sides in a trapezoid are the bases. The height can be found by drawing a right triangle within the trapezoid.

Kites and Rhombi:

A = 1/2(d1*d2)

The entire diagonal times the other entire diagonal divided by two gives us the area of a kite or rhombus.