Geometry Flashcards
distance from a point to the origin on a cordinate plane
√[(x-0)2 + (y-0)2]
√X2 + Y2
The third side of a triangle must be…
less than the sum of the other two sides and greater than their difference
sum of interior angles of a polygon
(n-2) x 180
area of a triangle
(base x height) /2
area of a rectangle
length x width
area of a trapezoid
(base1+ base2) x height / 2
area of a parallelogram
base x height
area of a rhombus
diangonal1 x diagonal2 / 2
surface area
the sum of all the areas of all the faces
volume of a cube
s3
volume of a rectangular solid
length x width x height
how many books each with x volume can be packed into a crate with y volume
cannot be determined without knowing the exact dimension of the books
the sum of angles of a triangle
180
if you are given two sides of a triangle, the length of the 3rd side…
must lie between the difference and the sum of the two given sides
common right triangles
3-4-5 (6-8-10, 9-12-15, 12-16-20)
5-12-13 (10-24-26)
8-15-17
45º-45º-90º triangle
1 : 1 : √2
x : x : x√2
this triangle is exactly half of a square
30º- 60º - 90º
1 : √3 : 2
x : x√3 : 2x
diagonal of a square
d = s√2
main diagonal of a cube
s√3
deluxe pythagorean threorem to find diagonal of a rectangular solid
d2 = x2 + y2 + z2
similar triangles (define)
triangles are defined as similar if all their corresponding angles are equal and their corresponding sides are in proportion
if two similar triangles have corresponding side lengths in ratio a:b, their areas will be…
their volumes will be…
a2 : b2
a3 : b3
special properties of equilateral triangles
can be split into two 30-60-90 triangles with the height of
(x√3)/2
area = (1/2)*S*(S√3/2)
=S2(√3/4)
On DS questions regarding the xy-plane, we can use any
of the following to find the others:
- Any single equation containing both x and y
- Slope-intercept form of the line
- Two points on the line
- The intercepts of the line
