Triangles & Diagonals Flashcards
(13 cards)
Triangle Sides Length Rule (+ and -)?
The 3rd side of a triangle must be less than the sum of the other two angles. Similarly, the 3rd side must be greater than (side 1 - side 2).
If two angles are the same, then what does that say about the length of their opposite side?
The sides must be the same length
When can I use Pythagorean Theorem?
Only with right triangles
What are the most common right triangles (Pythagorean Theorem short cut)?
3-4-5 (6-8-10/9-12-15/12-16-20)
5-12-13 (10-24-26)
8-15-17 (none)
GMAT Pythagorean Theorem Trick. GMAT will give you a triangle with sides 3-4 and ask you to figure out the length of the 3rd side. What is the trick?
The triangle is not a right triangle and therefore the shortcut (Pythagorean Theorem can not be used.)
What is the relationship of the lengths of a “______” isosceles triangle?
1:1:Square Root of 2
or
x:x:x square Root of 2
An equilateral triangle cut down the center forms what type of triangle and what are their corresponding angle degrees?
2 right triangles with sides 30-60-90.
What is the relationship of the lengths of a 30-60-90 triangle?
x : x square root 3 : 2x
short leg : long leg: hypotenuse
Formula for Diagonal of a square
D=side (square root of 2) ((isosceles triangle))
Sqare is 2D :: side (square root of 2)
Formula for Diagonal of a cube
D=side (square root of 3) ((30-60-90 long leg))
Cube is 3D :: side (square root of 3)
(Do the Pythagorean Triple to find the bottom diagonal of the bottom face. Then use that length as one of the sides (3riple again) to find the length of the true diagonal. )
Formula for the Diagonal of a rectangular solid (3C)
x^2+y^2+z^2=d^2
x,y,z are the 3 sides of the rectangular solid
What is the relationship between similar triangle side lengths and the area of the triangles?
If a corresponding side length is a:b of similar triangles, then their area will be a^2:b^2
Formula for area of an equilateral triangle (shortcut)
(S^2*square root of 3)/4
