Section 3.3 Proofs of Biconditional Statements
One of the logical equivalencies in Theorem 1.1 is the following one for biconditional statements.Proposition 3.3.
Suppose that
Proof.
We assume that we have a right triangle where
We first prove that if this right triangle is an isosceles triangle, then the area of the right triangle is
Hence,
We now prove the converse of the first conditional statement. So we assume the area of this isosceles triangle is
We now use the Pythagorean Theorem to conclude that
The last equation implies that
Since we have proven both conditional statements, we have proven that this right triangle is an isosceles triangle if and only if the area of the right triangle is