)} r@r@bFP rLr <r rvjxqrp@rr9YT
"p Ỳep0? `]de Given right triangle ABC, construct squares ADEC, CFGB, and BHIA external to the triangle. One side of each square is also a side of the triangle. Join vertices of the squares to form the triangles BGH, AID and CEF.
Define all four triangles as polygons and measure their areas. Note that area ABC = area BHG. No surprise, since these two are congruent. However note area AID = area ABC = area CEF. This is a mild surprise. Deform triangle ABC to discover these equalities are true for all shapes of ABC.
Question: Why is this?
Hint: Express the areas in terms of two sides and the included angle.
Mel Thornton, Univ of Nebraska-LincolnD
A2
A2!DP
d$P@
B OZT_A ỲepBBjZo_xB ỲepBBjoUUC ỲepCBNYo_BgBg
j ỲepBBBB?iYo*
k ỲepBBCB?NYo
m ỲepCBBB?:?E ỲepC'Bp ?F ỲepCCZ_G ỲepBCj?oD?H ỲepBBO?TDI ỲepBBu$z?D ỲepBB9o
m ỲepCBC'Bp?i?
k ỲepCCCB?iY_
k ỲepBBBC?i>o_?
j ỲepBBBB?N>T_
j ỲepBBBB?YTz?
m ỲepBBBB?t?~
n ỲepBBC'Bp?
9
p ỲepC'BpCC? Y
q ỲepBCCC?
N>oD
r ỲepBBBB?i>_
s ỲepBBBC?
>Tz
t ỲepBBBB?