Book I. Propositions 35 and 36
1. What does it mean to say that two figures --two triangles, two
To see the answer, pass your mouse over the colored area.
It means that the space enclosed by each boundary
2. a) State the hypothesis of Proposition 35.
Parallelograms are on the same base and in the same parallels.
2. b) State the conclusion.
Those parallelograms are equal.
2. c) Practice Proposition 35.
3. Prove Proposition 35 for the case where EB does not intersect DC.
3. Prove parallelograms ABCD, EBCF equal.
3. (Hint: Triangles EAB, FDC are again equal.)
Triangles EAB, FDC are again equal for the same reasons.
4. Prove that if the base of a parallelogram is doubled, then its area is
4. (Hint: I. 36.)
5. Prove that if the height of a parallelogram (that is, the distance