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Proof: By Euclid

(related to Corollary: Angles of a Right And Isosceles Triangle)

• By Prop 1.32, the sum of all angles in a plane triangle is $180^\circ.$
• If a right triangle is isosceles, then their angles are half of $180^\circ-90^\circ=90^\circ,$ i.e. a right angle.
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Thank you to the contributors under CC BY-SA 4.0!

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References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"