Polygons Unit Test

Interior angle sum

180(n-2)

Exterior angle sum

360

ONE interior angle of a regular polygon

180(n-2)/n

ONE exterior angle of a regular polygon

360/n

Opposite sides of a parallelogram are ____ and ____

congruent, parallel

Opposite angles of a parallelogram are ____

congruent

Consecutive angles in a parallelogram are ____

supplementary

In a parallelogram, the diagonals ____ each other

bisect

5 ways to prove that quadrilaterals are parallelograms

* opposite sides are congruent
* opposite sides are parallel
* one pair of opposite sides are congruent and parallel
* opposite angles are congurent
* diagonals bisect

A rectangle has four ____ angles

right

A rectangle’s diagonals are ____

congruent

In a rectangle, when the diagonals intersect, they create 4 smaller segments. These 4 segments are ____, which creates 4 ____ triangles

congruent, isosceles

A rhombus has four ____ sides

congruent

In a rhombus, the diagonals are ____, creating four ____ triangles

perpendicular, right

In a rhombus, the diagonals ____ both pairs of opposite angles

bisect

A square follows all of the properties of a ____, ____, and a ____

parallelogram, rectangle, rhombus

A trapezoid has exactly one pair of ____ sides, called ____

parallel, bases

If the two legs in a trapezoid are congruent, then it is ____

isosceles

In an isosceles trapezoid, the diagonals are ____

congruent

In an isosceles trapezoid, both pairs of ____ angles are congruent

bases

Trapezoid midsegment formula

average of the bases

Area of a regular polygon

A=1/2ap

Area of parallelogram

A=Bh

Area of rectangles

A=Bh

Area of squares

A=s^2

Area of rhombi

A=1/2d1d2

Area of trapezoids

A=1/2h(b1+b2)

Area of SSS triangles

A=\[square root\]s(s-a)(s-b)(s-c)

Area of SAS triangles

A=1/2bcsinA

A=1/2acsinB

A=1/2absinC

Area of equilateral triangles

A=\[radical\]3/4\*a^2

Semi perimeter (s) formula

A=1/2(a+b+c)

Geometric probability formula

Area of region B/Area of region A

Area of shaded region/Area of entire diagram

Coordinate Geometry

* Step 1 (parallelogram): Show that the diagonals bisect each other (using the midpoint formula to show that they have the same midpoint)
* Step 2 (rectangle): Show that all angles are 90 degrees (show that consecutive sides have opposite reciprocal slopes)
* Step 3 (rhombus): Show that the diagonals are perpendicular (opposite reciprocal slopes)
* Step 4 (square): Prove that it is a rectangle AND a rhombus

Midpoint formula

(x1+x2/2 , y1+ y2/2)

Slope formula

m=y2-y1/x2-x1

Distance formula

\[square root\](y2-y1)^2+(x2-x1)^2

The midsegment of a trapezoid is ____ to the bases

parallel