Euclid's Elements Book I

1. Let ABC be a triangle, and let one side of it, BC, be produced to D. The claim: the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC, and the three interior angles of the triangle, ABC, BCA, CAB, are equal to two right angles. (Try dragging the vertices.)
2. Through the point C let CE be drawn parallel to the straight line AB.

   Proposition I.31

   Proposition I.31: Through a given point to draw a straight line parallel to a given straight line.
3. Since AB is parallel to CE, and AC has fallen upon them, the alternate angles BAC, ACE are equal to one another.

   Proposition I.29

   Proposition I.29: A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles.
4. Again, since AB is parallel to CE, and the straight line BD has fallen upon them, the exterior angle ECD is equal to the interior and opposite angle ABC.

   Proposition I.29

   Proposition I.29: A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles.
5. But the angle ACE was also proved equal to the angle BAC; therefore the whole angle ACD is equal to the two interior and opposite angles BAC, ABC.

   Common Notion 2

   Common Notion 2: If equals be added to equals, the wholes are equal.
6. Let the angle ACB be added to each; then the angles ACD, ACB are equal to the three angles ABC, BCA, CAB. But the angles ACD, ACB are equal to two right angles; therefore the three angles of the triangle are also equal to two right angles.

   Proposition I.13

   Proposition I.13: If a straight line set up on a straight line makes angles, it will make either two right angles or angles equal to two right angles.

Being what it was required to prove.