
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 28th, 2017, 07:34 AM  #1 
Newbie Joined: Oct 2015 From: Eskişehir Posts: 11 Thanks: 0  Proof of four triangles with equal area.
I have been working on proofs without words, but I have a bit of a problem about Steven Snover's proof. It proves that these four triangles have equal area. Proof comes from rotation, but I couldn't get it. Last edited by skipjack; February 28th, 2017 at 08:36 AM. 
February 28th, 2017, 08:22 AM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 114 Thanks: 44 Math Focus: Dynamical systems, analytic function theory, numerics 
Here is a hint. The outside triangles each have 2 sides equal in length to 2 sides of the inner triangle and the angle between these sides is complimentary to the corresponding angle of the inner triangle.

February 28th, 2017, 08:45 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 17,172 Thanks: 1285 
Each particular rotated triangle aligns after rotation with the central triangle. The two triangles have the same height and the corresponding base lengths are the same, so the triangles have equal area.


Tags 
area, equal, proof, triangles 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Right angled triangles and area of a triangle  novelaholic  Geometry  4  October 4th, 2014 11:21 AM 
Area of Similar Triangles  Raye  Algebra  1  November 27th, 2013 02:42 PM 
ratio value of area between two triangles  Albert.Teng  Algebra  1  April 20th, 2013 05:47 AM 
An Area property of Triangles  elim  Algebra  0  September 1st, 2011 11:13 AM 
Area of Triangles in Trapezoid  Spaghett  Algebra  4  June 18th, 2011 10:24 PM 