Polygons- Math

Definition of a parallelogram

a quad with both pairs of opposite sides parallel

Name all thrms. about parallelograms

- parallelogram = opp. sides congruent

- parallelogram = opp. angles are congruent

- parallelogram = diags. of a parallelogram bisect each other

Name all the thrms. of proving a parallelogram

- both pairs of opp. sides congruent = parallelogram

- one pair of opp. side congruent + parallel = parallelogram

- both pair opp. angles congruent = parallelogram

- diags. bisect each other = parallelogram

- both pairs of opp sides parallel = parallelogram

What thrm supports this?

If 3 parallel lines cut off congruent segments on one transversal, then they cut of congruent segments on every transversal.

What thrm. makes this true?

A line that contains the midpoint of one side and is parallel to a second side passes through the midpoint of the third side.

Defn. rectangle

a quad with four right angles (it is a parallelogram)

Defn. Rhombus

a quad with four congruent sides (it is a parallelogram)

Defn. of a square

a quad with four congruent sides and four right angles (it is a parallelogram)

List all thrms. about rectangles

• diags. of a rectangle are congruent

• if an angle of a parallelogram is a right angle, then the parallelogram is a rect.

List all rhombus thrms.

• the diags of a rhombus are perp.

• each diag of a rhombus bisects 2 angles of the rhombus

• if two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus

Defn. of a trapezoid

A quad with exactly one pair of parallel sides

Defn. isosceles trapezoid

A trapezoid with congruent legs

Defn. of a kite

A quad with 2 pairs of consecutive congruent sides

Thrms. of a trapezoid

• the midsegment (median) of a trapezoid is the segment that joins the midpoints of the legs

  • the midsegment is parallel to the bases

  • the midsegment has a length equal to the median of the base lengths

List the thrms. of an isosceles trap

• base angles of an isosceles trap are congruent

• diags of an isosceles trap are congruent

List the thrms. for a kite

• diags of a kite are perp.

• the longer diag bisects shorter diag

• the longer diag bisects the angles

• the angles formed by non-congruent sides are congruent

Polygon

a closed figure with 3 or more sides and angles

Convex vs. Concave polygons

Convex - all angles in the polygon < 180

Concave - contains reflex angles >180

Thrm. about measures of convex polygon angles?

The sum of the measures of the angles of a convex polygon with n sides is 180(n-2)

What thrm makes this true?

The sum of the measure of the exterior angles of a convex polygon, one angle at each vertex, is 360.

Area formula for a regular polygon?

1/2 * a * P

Area formula for an equilateral triangle

s²√3/4

Herrons Formula

When your given SSS, use ______

herrons formula

Area formula for a quad with perp. diags

½ d1 d2

Area for a trapezoid`

mh

what is m in trapezoid formula?

m=b1*b2/2

area formula for a square

square: s²

area of a circle

πr²

circumference of a circle

2πr or πd

Lateral Area of a prism

ph

lateral area of a pyramid

½ Pl

lateral area of a cone

πrl

volume of a pyramid

1/3 bh

volume of a cone

1/3 πr² h

surface area of a sphere

4πr²

volume of a sphere

4/3 πr³

surface area of a hemisphere

3πr²

volume of a hemisphere

2/3 πr³

area formula for a parallelogram

bh