1. Prove proposition I.24. You are allowed to use the web site http://aleph0.clarku.edu/~djoyce/java/elements/elements.html as a resource.

2. Using the part of I.27 proved in class:

• If a transversal falling on two lines has a pair of alternate interior angles that are congruent, then the lines are parallel

Prove the other part of I.27 and the two parts of I.28

a. If a transversal falling on two lines has a pair of alternate exterior angles that are congruent, then the lines are parallel.

b. If a transversal falling on two lines has a pair of corresponding angles that are congruent, then the lines are parallel

c. If a transversal falling on two lines has a pair of interior angles on the same side of the transversal that are supplementary (which add up to 2 right angles) then the lines are parallel.

3. Do problem #7 in 2.3 N. The first step is to extend the median BE beyond the triangle, and construct a point B' on that line such that BE=B'E. The new triangles thus formed using B' should be useful.