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Feb 02, 2013 · 3)Proofs By cases or by exhaustion. Solve Proving Proofs -Indirect Proof: Instead of proving the proposition directly, we establish the proof of the proposition through proving a proposition which is equivalent to the given proposition. 1)Proofs by contradiction. 2)Proofs by using contrapositive statement. 3)Proofs by a by a counter example. The precise statements of the conjectures are given below. Each conjecture has a linked Sketch Pad demonstration to illustrate its truth (proof by Geometer's Sketch Pad!). The linked activities sheet also include directions for further "hands on" investigations involving these conjectures, as well as geometric problems which utilize their results.