Plane Geometry Flashcards
Plane geometry: adding and subtracting lengths
best way to start is to mark up the figure, put as much info from the question into the figure that you can. then plan and solve
triangle
three sided polygon
Sum of interior angles of triangles
all three angles equal 180
Measure of an exterior angle of triangles
the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
sum of the exterior angles of triangles
the measure of three exterior angles of any triangle add up to 360 degrees
area formula of a triangle
1/2(base)(height)
what is the height of a triangle
the height is perpendicular distance between the side that’s chosen as the base and the opposite vertex
triangle inequality theory
the length of any one side of a triangle must be greater than the positive difference and less than the sum of the lengths of the other two sides.
Similar triangles
triangles that have the same shape: corresponding angles are equal and corresponding sides are proportional.
three special triangles
isosceles, equilateral, and right triangles
isosceles triangle
an isosceles triangle is a triangle that has two equal sides. Not only are two sides equal, but the angles opposite the equal sides, called base angles, are also equal.
equilateral triangle
an equilateral triangle is a triangle that has three equal sides and equal angles.
area of a equilateral triangle
s^2sqrt(3)/4 s being a side
right triangle
a right triangle is a triangle with a right angle. the two sides that form the right angle are called legs
Pythagorean theorem
you find the length of any side of a right triangle using a^2+b^2=c^2
Pythagorean triplet
a set of integers that fits the Pythagorean theorem, the simplest is 3,4,5. any integers in a 3:4:5 ratio make up a triplet.
hidden special triangles
key to solving a lot of geometry problems is to add a line segment or two to the figure. then find some special characteristics of triangles
Trapezoid
a four-sided figure with one pair of parallel sides and one pair of nonparallel sides.
area of a trapezoid
{(base1+base2)/2}x height
average of the parallel sides and the perpendicular side for height
Parallelograms
a parallelogram is a four-sided figure with two pairs of parallel sides. opposite sides are equal, opposite angles are equal.
area of parallelogram
base*height
rectangle
a rectangle is a four sided figure with four right angles. opposite sides are equal.
area of a rectangle
length * width
Rhombus
a four sided figure with four equal sides (like a parallelogram but equal
square
four sided figure with four right angles and for equal sides.
area of square
(side)^2
area of a hexagon
[3s^2sqrt(3)]/2
circumference of a circle
the total distance around the circle.
=2pieR
=pieD
r radius and d diameter
Length of an arc
an arc is a piece of the circumference. if n is the degree measure of the arcs angle then the formula is
(n/360)(2pieR)
Area of a circle
pieR^2
area of a sector
sector is a piece of the area of a circle.
n/360)(pieR^2
