GRE Review: Triangle Geometry

4 months ago\({\bf{Memorization~List:}}\) - all triangles have angles that sum up to 180 - the exterior angle on a triangle is equal to the sum of the two non-adjacent angles |dw:1540347361202:dw| so in the above example, angles 4 and 5 would both be equal to (angle 1 + angle 2) if you don't remember this fact you can always verify manually angle 1 + angle 2 + angle 3 = 180 since they're three angles in a triangle angle 3 + angle 4 = 180 subtracting angle 3 from both equations gives us angle 1 + angle 2 = 180 - angle 3 angle 4 = 180 - angle 3 so angle 4 = angle 1 + angle 2 same logic extends to angle 5

4 months ago- side length rules: let a, b, and c be the lengths of a triangle > a^2 + b^2 = c^2 gives a right triangle. note that this is the pythagorean theorem > a^2 + b^2 < c^2 gives an acute triangle > a^2 + b^2 > c^2 gives an obtuse triangle > the sum of any two sides must be greater than the third side, or in other words a + b > c a + c > b b + c > a if any of these conditions fails then the triangle is not valid and could not actually exist > the difference of the lengths must be less than the third side, or in other words a < |c - b| b < |a - c| c < |b - a|

4 months agospecial triangles: memorize these angles and proportions to save yourself time w/ calculations |dw:1540348348998:dw| these can be derived w/ pythagorean theorem in a pinch special formulas: area of triangle = (1/2)bh, make sure the height is drawn perpendicularly from the base otherwise it won't work area of an equilateral triangle: you can calculate the height using the pythagorean theorem but as a shortcut, if you know the side length, it's A = (sqrt(3)/4 ) s^2

4 months agoAdapted from Barron's test prep book for the new GRE, 19th edition

4 months ago