Geometry

Question 6

Question 5

Question 2 shown below:

Suppose you know that both have right angles (at vertices A and D respectively), and that AB = DE, and BC = EF. Now write out a complete proof that the two triangles are congruent. For your proof, please just use the results we have from Euclid up to this point – i.e. just the results of Propositions 1 through 34. As Andy showed in class, probably the simplest way to begin the proof is to start with triangle ABC, and then explain how to construct a triangle to its left, sharing side AB, as in the diagram below, in such a way so that you can show that the second (blue) triangle is congruent to triangle DEF. Next, show the blue triangle is congruent to the red triangle... On the other hand, feel free to try approaching this proof in a completely different way if you'd like!