chapter 7 math

parallelogram opposite sides theorem

if a quaderilateral is a parallelogram, then its opposites sides are congruent

parallelogram opposite angles theorem

if a quadrilateral is a parallelogram, then its opposite angles are congruent

parallelogram consecutive angles theorem

if a quadrilateral is a parallelogram, then its consecutive angles are supplementary

parallelograms diagonals theorem

if a quadrilateral is a parallelogram, then its diagonals bisect eachother

diagonal

a segment that joins two non-adjacent verticies

polygon

a closed plane figure formed by 3 or more sides

polygon interior angles theorem

the sum of the measures of the interior angles of a convex n-gon is (n-2) x 180

corollary to the polygon interior angles theorem

the sum of the measures of the interior angles of a quadrilateral is 360

regular polygon

a convex polygon that is both equilateral and equiangular

polygon exterior angles theorem

the sum of the measures of the exterior angles of a polygon equal 360

how to find sum of exterior angles

1) find sum of the interior angle measure(n-2)x 180

2)Find measure of each interior angle if its is regular(divide total sides by sum of int. angle measure)

3/ find the measure of each exterior angle(180 minus each int. angle)

4) what is the sum of the measure of exterior angles(measure of each ext. angle x side number)

find interior SUM of regular polygon from EACH interior angle

1)find exterior angle

2)divide by 360

3)use (n-2) x 180 to get into. angles

parallelograms opposite sides convers

if both pairs of opposite side of a quadrilateral are congruent then the quadrilateral is a parallelogram

parallelogram opposite angles converse

if both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram

opposite sides parallel and congruent theorem

if one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram

parallelogram diagonals converse

if the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallogram

square

parallelogram with 4 congruente sides and 4 congruente angles

a rhombus and a rectangle

rectangle

parallelogram with 4 congruent angles

rhombus

parallelogram with 4 congruente sides

rhombus diagonals theorem

a parallelogram is a rhombus if and only if its diagonals are PERPENDICULAR/ANGLES ARE 90

rhombus opposite angles theorem

a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles

rectangle diagonal theorem

a parallelogram is a rectangle if and only if its diagonals are CONGRUENT

how to find if points are a rectangle rhombus or square)

1) plot said points

2) find the length diagonals(find if they are equal)

3) check slopes(if perpendicular)

Trapezoid

Has exactly ONE pair of parallel sides(bases)

Base angles congruent

2 sets of base angles (one for each base)

Non parallel sides called legs

If legs are congruent the the trapezoid in an isosceles trapezoid

How to find out if an trapezoid is isosceles on graph

1) check opposite side slopes(only some set can be parallel)

2) check length of legs(if congruent they are isosceles (

Isosceles trapezoid base angles theorem

If a trapezoid is isosceles then each pair oof base angles is congruent

Isosceles trapezoid base angles converse

If a trapezoid has a pair of congruent base angles then it’s an isosceles

Isosceles trapezoid diagonals theorem

A trapezoid is isosceles if and only if its diagonals are CONGRUENT

The ——- of a trapezoid is the segment that connects the midpoints of the legs

Midsegment

Trapezoid mid segment theorem

The mid segment of a trapezoid is parallel to each base and its length is half e of the sum of the length

kite

Quadrilateral with TWO pairs of consecutive congruent sides

Opposite sides are not congruent

Diagonals PERPENDICULAR

Kite diagonals theorem

If a quadrilateral is a kite then its diagonals are perpendicular

Kite opposite angles theorem

If a quadrilateral is a kite then exactly ONE pair of opposite angles are congruent

Diagonals bisect opposite angles

Rhombus and square

Diagonals perpendicular

Rhombus and square and kite

Diagonals are congruent

Rectangle and square and isosceles trapezoid