Geometry Flashcards
vertices (polygons)
endpoints of the sides that meet
how many triangles can a polygon be divided into
n-number of sides
n-2
how to find sum of interior angles of a polygon
(n-2)(180º)
Regular polygon
all sides and all angles are congruent
How to find the angles of a regular polygon when you know the sides
(n-2)(180) = x
x/n = degree of each angle
Triangles
sum of interior angles = 180º
length of each side is less than the sum of the other 2 sides
equilateral triangle
3 congruent sides
3 congruent angles (60°)
isosceles triangle
2 congruent sides
angles opposite the congruent sides are congruent
right triangle
has interior right angle
hypotenuse is the side opposite the right angle
other sides are legs
Pythagorean theorem
hypotenuse2 = leg12 + leg22
ratio of sides of an isosceles right triangle
1 : 1: √2
y2 = x2 + x2
y2 = 2x2
y = √2x
30° 60° 90° triangle
half of an equilateral triangle
ratio of sides of a 30-60-90 triangle
1: √3: 2
x2 + y2 = (2x)2
x2 + y2 = 4x2
y2 = 3x2
y = √3x
Area of triangle
A = (bh)/2
base x height
- any side can be the base
- height is a perpendicular line from base to opposite vertex
3 ways to tell if two triangles are congruent
- if 3 sides of one triangle are congruent to the other
- if 2 sides and its angle are congruent on each
- if 2 angles and a side are congruent
similar triangles
same shapes but not necessarily the same size
you can match up the vertices so the angles are congruent
OR
the lengths of corresponding sides have the same ratio
(all 30-60-90° triangles are similar)
proportions of similar triangles ABC and DEF
AB = BC = AC
DE = EF = DF
sum of interior angles of a quadrilateral
360°
rectangles
4 right angles
opposite sides are parallel and congruent
2 interior diagonals are congruent
if all four sides are congruent its a square
parallelogram
both pairs of opposite sides are parallel
opposite sides are congruent and opposite angles are congruent
trapezoid
2 opposite sides are parallel
A = 1/2 (b1 + b2)(h)
bs are corresponding sides
Area of all parallelograms
A=bh
any side can be base
height is perpendicular line reaching to the other side
Diameter =
2r
radii
radii of congruent circles
equal radii
chord
any line segment joining to points on the circle
circumference
distance around the circle
C/d = π
or
C = dπ
or
C = 2πr
finding the length of an arc on a circle
ratio of arc length to circumference are the same as the ratio of inner arc degree to 360°
length of arc ABC = arc°
circumference = 360°
Area of a circle
πr2
tangent
line that intersects a circle at exactly one point
radius is perpendicular to tangent lines
rule about triangles inscribed in circles
if one side of an inscribed triangle is a diameter of the circle then the triangle is a right triangle
(vice versa: a right triangle inscribed inside of circle then one side of it is the diameter)
rectangular solids
6 faces
12 edges
8 vertices
volume of rectangular solid
V = l x w x h
surface area of a rectangular solid
sum of face areas
A = 2 (lw + lh + wh)
cube
6 square faces
l = w = h
Axis of cylinder
line that joins the 2 centers of the circles (its height)
right circular cylinder
axis is perpendicular to bases
volume of cylinder
V = πr2h
Surface area of cylinder
(2πr2) + 2πrh
