make a conjecture about the diagram below. is ac greater than, less than, or equal to bc? explain your…

Explanation:

Step1: Recall right - triangle property

In right - triangle $\triangle ABC$, $\angle ABC = 90^{\circ}$.

Step2: Apply the Pythagorean theorem

In $\triangle ABC$, by the Pythagorean theorem, $AC^{2}=AB^{2}+BC^{2}$. Since $AB>0$, then $AC^{2}>BC^{2}$.

Step3: Compare the lengths

Taking the square root of both sides of the inequality $AC^{2}>BC^{2}$ (and considering that $AC>0$ and $BC>0$), we get $AC > BC$.

Answer:

$AC$ is greater than $BC$.