Write an indirect proof that an obtuse triangle does not have a right angle.

Given: Triangle RST is an obtuse triangle.
Prove: Triangle RST does not have a right angle.

Let angle S be an obtuse angle. Assume Triangle RST has a right angle. Let angle R be a right angle. Use direct reasoning to lead to a contradiction.

To prove that Triangle RST does not have a right angle, we will use an indirect proof.

First, we are given that Triangle RST is an obtuse triangle, which means that at least one of its angles is greater than 90 degrees.

Assume, for the sake of contradiction, that Triangle RST also has a right angle. Let's assume that angle R is the right angle.

Since angle R is a right angle, it measures exactly 90 degrees.

Now, if Triangle RST has a right angle at R, and it is also an obtuse triangle, then it must have another angle that is greater than 90 degrees. Let's call this angle S.

Since S is an obtuse angle, it must be greater than 90 degrees. However, we assumed that angle R is a right angle and measures exactly 90 degrees.

Here we have a contradiction, as angle S cannot be greater than 90 degrees if angle R is exactly 90 degrees. This contradicts the assumption that Triangle RST has a right angle.

Therefore, our assumption that Triangle RST has a right angle is false.

Thus, we can conclude that Triangle RST does not have a right angle, as required to prove.