Euclid's Elements Book I

1. Let ABC be the given triangle, and D the given rectilineal angle. It is required to construct in the rectilineal angle D a parallelogram equal to the triangle ABC. (Every point can be dragged, including the arms of the angle D.)
2. Let BC be bisected at E, and let AE be joined.

   Proposition I.10Postulate 1

   Proposition I.10: To bisect a given finite straight line.

   Postulate 1: To draw a straight line from any point to any point.
3. On the straight line EC, at the point E on it, let the angle CEF be constructed equal to the angle D.

   Proposition I.23

   Proposition I.23: On a given straight line and at a point on it to construct a rectilineal angle equal to a given rectilineal angle.
4. Through A let AG be drawn parallel to EC, and through C let CG be drawn parallel to EF. Then FECG is a parallelogram.

   Proposition I.31

   Proposition I.31: Through a given point to draw a straight line parallel to a given straight line.
5. Since BE is equal to EC, the triangle ABE is equal to the triangle AEC; therefore the triangle ABC is double of the triangle AEC.

   Proposition I.38

   Proposition I.38: Triangles which are on equal bases and in the same parallels are equal to one another.
6. The parallelogram FECG is on the same base with the triangle AEC and in the same parallels, so it too is double of AEC. Therefore FECG is equal to the triangle ABC, and it has the angle CEF equal to the angle D.

   Proposition I.41Common Notion 1

   Proposition I.41: If a parallelogram have the same base with a triangle and be in the same parallels, the parallelogram is double of the triangle.

   Common Notion 1: Things which are equal to the same thing are also equal to one another.

Being what it was required to do.