math unit on polygons

properties of a parallelogram

1. opp sides are congruent

2. opp angles are congruent

3. consecutive angles are supplementary(180)

4. diagonals bisect each other

properties of rectangles

1. all four angles are right angles

2. diagonals are congruent

3. parallelogram properties

properties of a rhombus

1. diagonals are perpendicular

2. diagonals bisect opp angles

3. parallelogram properties

properties of a square

1. all sides and angles equal

2. diagonals bisect each other at a 90 degree

3. diagonals equal in length

4. all properties (8 plus these)

interior angle sum formula

sum = ((number of sides) - 2) x 180

regular polygon

all side measures are congruent so all angle measures are congruent

sum of ext. angles of any polygon

360 degrees

method 1: prove both pairs of opp sides are congruent

if AB is congruent to CD and DA to BC then ABCD is a parallelogram: use distance formula

distance formula

d = square root of (x2-x1)² + (y2-y1)²

method 2: prove both pairs of opp sides are parallel

if AB is parallel to CD and AD is parallel to BC then ABCD is a parallelogram: use slope formula

slope formula

m = (y2-y1) over (x2-x1)

method 3: prove one pair of opp sides are congruent and parallel

If AB is congruent to CD and AB is parallel to CD then ABCD is a parallelogram