Proposition 5.
In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines be produced further, the angles under the base will be equal to one another.
Let ABC be an isosceles triangle having the side AB
equal to the side AC; and let the straight lines BD, CE be produced further in a straight line with AB, AC. [Post. 2] I say that the angle ABC is equal to the angle ACB, and the angle CBD to the angle BCE.
Let a point F be taken at random on BD; from AE the greater let AG be cut off equal to AF the less; [I. 3] and let the straight lines FC, GB be joined. [Post. 1]
Then, since AF is equal to AG and AB to AC,
therefore the two sides BF, FC are equal to the two sides CG, GB respectively; and the angle BFC is equal to the angle CGB,
and the remaining angles will be equal to the remaining