Triangles Flashcards
Special triangles
3-4-5 (6-8-10) (9-12-15) (12-16-20) (15-20-25)
5-12-13 (10-24-26)
8-15-17
7-24-25
Sides of a 30 60 90 right triangle
X, x root 3, 2x
Sides on a 45 45 90 triangle
X, X, X root 2
Difference between squares
(X+y) (x-y) =x^2-y^2
Can use this to find one side of a right triangle
A triangle is acute (3 angles less than 90) when
A^2+B^2>C^2
A triangle is obtuse (has one angle greater than 90) when
a^2+b^2
Triangle inequality theorem
The sum of any 2 sides of a triangle must be greater than the 3rd. Also the difference of any 2 sides must be less than the 3rd.
The measure of an exterior angle in a triangle =
The sum of the 2 opposite interior angles
45 45 90 shortcuf
To determine the leg lengths of a 45 45 90 triangle who hyp lacks a root 2, cut the hyp in half and multiple by root 2
Sum of the interior angles of any polygon
(N-2)180
Sum of the exterior angles of any polygon is always
360
Interior angles in a quadrilateral
360
Area of a trapezoid
Average of bases ×height
Volume of a rectangular solid
Length ×width×height
Diagonal of a rectangular solid
Root l^2+w^2+h^2
Diagonal of a cube
S root 3
Rhombus area (parallelogram with 4 equal sides)
=.5 (diagonal1 × diagonal 2)
Slope
Y2-y1/x2-x1
Two triangles are similar I’d
- 2 angles are identical
- All 3 legs are proportional or
- 2 legs are proportional and the angle between them is identical
If a right triangle is composed of 2 smaller right triangles..
All 3 are similar
How many triangles can you break a regular hexagon into ?
An octagon?
hexagon 6
Octogon 8
