Write an indirect proof in paragraph form.

Given: $AT=BT=5;CT=4$

Prove: $\angle ACB$is not a right angle.

An indirect proof is a proof wherein you begin by assuming temporarily that the desired conclusion is not true which then by reasoning logically reaches to a certain contradiction or some other known fact.

1. Assume temporarily that the conclusion is not true.

2. Reason logically until you reach a contradiction.

3. Point out that the assumption was wrong and the conclusion must then be true.

In order to write an indirect proof to prove that $\angle ACB$is not a right angle assume temporarily that the conclusion above is untrue.

Proof: Assume temporarily that$\angle ACB$ is a right angle.

By the property of right angles triangles,

$\begin{array}{c}A{B}^2=A{C}^2+B{C}^2\\ {10}^2=6^2+8^2\end{array}$

There can be only 2 cases: $AC=6,BC=8\text{\hspace{0.33em}\hspace{0.33em}or\hspace{0.33em}\hspace{0.33em}}AC=8,BC=6$.

Two triangles with two of its sides of dimension 4 and 5 cannot have the third side of a different dimension. Hence, initial assumption that$\angle ACB$ is a right angle is incorrect.

Therefore, it is proved that$\angle ACB$ is not a right angle.