Return to Euclid’s Elements of Geometry
If in a triangle two angles are equal to one another, the sides which subtend the equal angles will also be equal to one another.
Let ABC be a triangle having the angle ABC equal to the angle ACB;
I say that the side AB is also equal to the side AC.
For, if AB is unequal to AC, one of them is greater.
Let AB be greater; and from AB the greater let DB be cut off equal to AC the less; let DC be joined.
Then, since DB is equal to AC, and BC is common, the two sides DB, BC are equal to the two sides AC, CB respectively;
and the angle DBC is equal to the angle ACB;
therefore the base DC is equal to the base AB, and the triangle DBC will be equal to the triangle ACB, the less to the greater: which is absurd.
Therefore AB is not unequal to AC;
it is therefore equal to it.
Therefore etc.
Q.E.D.
Return to Euclid’s Elements of Geometry
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