Act Geometry notes

geometry notes to memorize

the formula for the area of a circle

*r is the radius*

the radius of circle

is half of the dimeter

to simplify a rotation in

rewrite it in fraction form

what does the pythagorean theorem state?

a2+b2=c2, where a and b are the lengths of the legs at a right triangle with a hypotenuse of length c.

the length of a line segment is?

the sum of the lengths of its parts

the formula for the circumference of a circle

c=2 3.14r where r is the length of the radius. the diameter of a circle is twice the length of the radius.

when given the circumference of c, it is:

efficient to calculate the length of the diameter d with the formula c=3.14d

the circumference of a circle is:

equal to 3.14 times the length of the diameter.

the diameter of a circle is:

a segment that passes through the center and has end points on the circle.

the midpoint formula

(xm,ym) = coordinates of the midpoint.
(x1, y1,) = coordinates of the first point.
(x2, y2) = coordinates of the second point.

when parallel lines are intersected by another line (called a transversal) the pairs of alternate interior angles are called?

congruent

the measures of the interior angles sum up to?

180

additional notes.

the tangent ratio is only defined for an acute angle of a right triangle. so it may be necessary to first draw the missing side to complete a right

additional notes.

the tangent of an acute angle is a right triangle is equal to the ratio of a the length of the leg opposite the angle to the length of the leg adjacent to the angle.

when parallel lines are cut by transversal, the following pairs of angles are formed:

congruent corresponding angles.
congruent alternate interior angles.
supplementary consecutive interior angles.

additional notes.

the diagonal of a rectangle divides the rectangle into two congruent right triangles.

additional notes.

use the Pythagorean theorem to find the length of a diagonal of a rectangle.

the equation of a circle in standard form:

(h, k) is the center and r is the radius

Sine =

Opposite/Hypotenuse

Cosine

Adjacent/Hypotenuse

Tangent

Opposite/Adjecent

Isosceles Triangle

an ***isosceles triangle*** is a triangle that has two sides of equal length.

Equilateral Triangle

an ***equilateral triangle*** is a triangle in which all three sides have the same length.

Right Angled Triangle

Right triangles are triangles in which one of the interior angles is 90 degrees, a right angle.

Rhombus

__parallelogram__ with opposite equal acute angles

Quadrilateral

1. a four-sided figure.

Trapezoid

a __quadrilateral__ with only one pair of parallel sides.

Parellelogram

a parallelogram is a simple quadrilateral with two pairs of parallel sides.

Pentagon

five sides and five angles

The formula for an area of a triangle

1/2**Base*Height*

Area of a Rectangle

Length\*Width

Length x Width x Height

Length x Width x Height = Volume of Cuboid

The formula for the volume of a sphere

4/3*pi*radius 3

Area of a trapezoid

1/2\**(Base1+base2)*Height*

if you have coordinates that are Vertical and Horizontal

Horizontal and vertical shifts are independent (ie, do not affect each other), so it is possible to calculate the result of both translations in a single step.

Area of a triangle

= 1/2 x base x height

angles of a triangle add up to?

180

area of a rectangle

A=length*width

Volume of a cylinder

V = πr²h