Triangles (6) Flashcards
Right triangle types
3/4/5; 6/8/10; 5/12/13; 10/24/26; 8/15/17; 7/24/25
30-60-90 side ratio
x (opp 30) : x rt 3 (opp 60) : 2x (opp 90)
All angles sum to
180
Third side triangle rule…
Sum of any two sides of a triangle must be greater than the third side.
Supplementary angle rule…
Sides opposing the supp angle given will add up to the supp angle.
Any side of a triangle is…
Greater than the diff and less than the sum of the two sides
Area of an equilateral triangle…
(s^2 rt 3) / 4
Equilateral triangles are…
By definition, isosceles
Right triangle with 45% alt angles ratio…
x : x : xrt2
Similar triangles
If two triangles have the same angles, their sides and heights are proportional. If two triangles have proportional sides, their angles are the same
Triangle in a circle
If two sides are radii, must be isosceles
When a line extends past the triangle
Look for similar triangles
If sides of similar triangles are in the ratio x:y…
Areas are in ratio x^2y^2
In order to apply right triangle ratios…
You must know which side is the hypotenouse
Area proportion on sim triangles is the sq of the side proportion. Therefore…
Side proportion must be sqrt of the area proportion
