Quadrilateral and Polygons

Polygon

A closed figure (in a plane) with 3 or more line segments as sides

Diagonal

a segment that connects vertices that are not consecutive

Non convex

interior and exterior diagonals (at least on part of diagonal is outside)

Convex polygons

all diagonals are inside

Sum for interior angles

(number of angles - 2) x 180

Sum of exterior angles

convex outside angles are always 360

Regular polygon

All sides and all angles are congruent

parallelogram

a quadrilateral with two pairs of parallel sides

if a quad is a p-gram, then the opposite sides are congruent

if a quad is a p-gram, then the opposite sides are congruent

if a quad is a p-gram, then the opposite angles are congruent

if a quad is a p-gram, then the opposite angles are congruent

if a quad is a p-gram, then the consecutive (same side) interior angles are supp

if a quad is a p-gram, then the consecutive (same side) interior angles are supp

if a quad is a p-gram, then the diagonals bisect each other

if a quad is a p-gram, then the diagonals bisect each other

If 3 or more parallel lines cut off congruent segments, then they cut off congruent segments on the other transversal

If 3 or more parallel lines cut off congruent segments, then they cut off congruent segments on the other transversal

In a quad if both pair of opposite sides are congruent then it’s a p-gram

In a quad if both pair of opposite sides are congruent then it’s a p-gram

In a quad if both pairs of opposite angles are congruent then it’s a p-gram

In a quad if both pairs of opposite angles are congruent then it’s a p-gram

In a quad, if one interior angle is supp to both of it’s consecutive angles then the quad is a p-gram

In a quad, if one interior angle is supp to both of it’s consecutive angles then the quad is a p-gram

In a quad if the diagonals bisect each other then the quad is a p-gram

In a quad if the diagonals bisect each other then the quad is a p-gram

In a quad if one pair of opposite sides is congruent and parallel then the quad is a p-gram

In a quad if one pair of opposite sides is congruent and parallel then the quad is a p-gram

Rectangle

a parallelogram and all rights angles that are congruent

Rhombus

a parallelogram that has all four sides congruent.

Square

a parallelogram with congruent angles and congruent sides

If rhombus..(property 1)

diagonals are perpendicular

If rhombus (property 2)

diagonals bisect pair of opposite angles

if rectangle (property 1)

if rectangle then diagonals are congruent

If diagonals of a parallelogram are perpendicular, then it is a rhombus

If diagonals of a parallelogram are perpendicular, then it is a rhombus

If one diagonal of a parallelogram bisects a pair of opposite angles, then it is a rhombus

If one diagonal of a parallelogram bisects a pair of opposite angles, then it is a rhombus

If the diagonals of a parallelogram are congruent, then it is a rectangle

If the diagonals of a parallelogram are congruent, then it is a rectangle

every property of a rhombus and a rectangle is a

square

Trapezoid

a quad with exactly one pair of parallel sides

The parallel sides of a trapezoid are called

bases

the non parallel sides of a trapezoid are called

legs

every angle within a trapezoid is called the

base angle

Isosceles trapezoid

a trapezoid with congruent legs

Isosceles trapezoid properties

opposite base angles that are supplementary

if isosceles then diagonals are congruent

isosceles trap theorem

If isosceles is a trapezoid then each pair of base angles are congruent

Midsgement of a trapezoid

a segment that connects the midpoints of the legs in a trapezoid

trapezoid mid segment theorem

1. midesgement parallel to bases

2. misegment is 1/2(b₁+b₂)

kite

a quadrilateral with two pairs of consecutive sides that are congruent, but no opposite sides congruent

The diagonals of a kite are

perpendicular

the opposite angles of a kite

are congruent expect for the top and bottom angles which are congruent to each other when cut in half

a kite has triangles that are

congruent

the parts of a diagonal going from left to right in a kite is

congruent

slope

y₂-y₁

_{______}

x₂-x₁

to find If a quad is a specific quad look for

slopes congruent = parallel, angles right, slopes opposite reciprocal then the angles are right

midpoint formula

/X₁+X₂ Y₁+Y₂ \

_{|———— ————- |}

_{\ 2 , 2 /}

distance formula

go form start of point to the end and then use Pythagorean theorem

when showing how a quad is a specific quad you give

reasoning just like a proof