TITLE: Prove that the area of the trangles are equal.
QUESTION [7 upvotes]: Prove that the area of all the traingles in the figure below are equal.

I tried using geogebra to determine an arbitrary values of $a$ , $b$, and $c$. I found out that the triangles have equal measure of area.

REPLY [8 votes]: Let 

$*sbh$ stands for triangles have same base and height. 
$*c$ stands for triangles are congruent. 

We have

$A_1 \stackrel{*sbh}{=} B_1 \stackrel{*c}{=} B_3 \stackrel{*c}{=} A_3$,
$A_3 \stackrel{*c}{=} B_3 \stackrel{*c}{=} B_4 \stackrel{*sbh}= A_4$,
$A_2 \stackrel{*c}= A_3$