Properties of Triangles

Since our midterm exam is on a lot of trigonometric stuff. I decided that I would go over some properties of triangles and quadrilaterals.

• The sum of the angles in a triangle add up to 180°
  
• The sum of the angles in any polygon other than a triangle add up to 360°
  
• Equilateral triangles have equal sides
  
• All equilateral triangles are equiangular, therefore, their angles are always 60°
  
• An isosceles triangle has at least two equal sides. Therefore, an equilateral triangle is an isosceles triangle.
  
• The perpendicular height of an isosceles triangle cuts the base into two equal pieces.
  
• The perpendicular height of an isosceles triangle cuts the upper angle into two equal angles.
  
• Two angles opposite any two equal sides are congruent(and vice-versa)
  
• The altitude of an isosceles triangle cuts the triangle into two right triangles, which can be used with trigonometric properties such as SOH CAH TOA and CHO SHA CAO
  
• The law of sines and cosines can be applied to a quadrilateral's diagonals to find the total area or perimeter of a quadrilateral.
  

I am still having trouble with simplifying trigonometric equations and "more difficult trigonometric equations" I seem to have trouble bringing the identities into context with the actual simplification of the equation.