The fifth proposition proves the base angles theorem, stating that the base angles of an isosceles triangle are equal. Euclid also proves that when the equal sides of the triangle are extended, then the exterior angles below the base angles are equal. This might seem like an immediate consequence of the first statement, but Euclid hasn't yet proved supplementary angles. First, Euclid selects on arbitrary point F on BD, and uses proposition 2/3 to transfer BF onto CE. By SAS congruence, △ABC is congruent to △ACD, which proves the purple lengths, purple angles, and green angles are congruent. Using SAS again, △BCD is congruent to △CBG, proving the yellow and blue angles are congruent. Since both the green angles and the yellow angles are congruent, the red angles must also be congruent.