Saltire Software

An Isosceles Triangle Theorem

In the figure, HEG is an isosceles triangle with EH = EI.

Also HF = GI.

A is the intersection of GF and HI.

The theorem states that AF = FG.

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FH
EH/EI
HI
FA
AG
HA
AI
HA/AI

We also see the ratio of HA/AI. Can you come up with a formula for this
ratio in terms of EH, EI and FA?

App generated by Geometry Expressions