Geometry Problem 1338: Four Squares, Diagonals, Angle, 45 Degrees, Areas. Math Infographic.

In the figure bellow, ABCD is a square and the measure of the angle EAF is 45 degrees (E and F lie on BD). If S₁, S₂, and S are the areas of the squares of diagonals BE, FD, and EF, respectively, prove that S = S₁ + S₂.

See solution below

Typography of Problem 1338 on Instagram:

#Geometry Problem 1338: Four Squares, Diagonals, Angle, 45 Degrees, Areas, #Typography #iPad Apps  http://www.gogeometry.com/school-college/4/p1338-square-45-degrees-diagonal-area-art-ipad-sw-apps.htm  #geometricart #fractals #sketch #drawing #proof #math #highschool

A post shared by Antonio Gutierrez (@gogeometry1) on Feb 27, 2018 at 1:42pm PST

 

Problem 1338 on Twitter:

#Geometry Problem 1338: Four Squares, Diagonals, Angle, 45 Degrees, Areas, #Typography #iPad Apps https://t.co/R6XhdwsOgs #geometricart #fractals #sketch #drawing #proof #math #highschool pic.twitter.com/eqZYFwx9ZO

— Antonio Gutierrez (@gogeometry) February 27, 2018

 

See also:
Art of problem 1338
Typography of problem 1338
Art of problem 1338: Hyperbolic Kaleidoscope
Art of problem 1338: Deform around a spiral.