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The two triangles in Fig. 1 have all three sides equal.
AB = PQ, BC = QR, CA = RP
In the following Fig. 2 triangles are constructed that also have three sides equal.
Draw a line segment FG equal in length to BC
Draw a circle centred at F with radius = AB
Draw a circle centred at G with radius = AC
These circles intersect at only two points, E and H
Connect FE, FH, GE, GH and EH
^FEH = ^FHE (∇EFH is isosceles as EF = EH)
^GEH = ^GHE (∇EGH is isosceles as EG = GH)
So
^FEG = ^FHG
So
∇FEG = ∇FHG (Two sides & inc. ang. equal)
Fig.1
Fig.1
Fig. 2
Fig. 2
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