Question

kyle is trying to prove that $\triangle abc$ is a right triangle. what is the best strategy for kyle to use?
use the distance formula to find the lengths of ab and bc. perpendicular lines have the same length.
use the slope formula to prove that ab $perp$ bc; therefore, angle abc is a right angle. then, use the distance formula to prove that ab $cong$ bc.
use the slope formula to prove that $abperp bc$; therefore, $angle abc$ is a right angle.
use the distance formula to find the lengths of ab, bc, and ac. then, substitute the side lengths into the pythagorean theorem.

Explanation:

To prove a triangle is a right - triangle, one can use the Pythagorean Theorem which states that in a right - triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. Finding side lengths using the distance formula and then substituting into the Pythagorean Theorem is a valid approach. The first option about perpendicular lines having the same length is incorrect. Proving perpendicularity using slopes and then proving side - length equality is not the best way to prove it's a right - triangle. Just proving perpendicularity using slopes doesn't fully prove it's a right - triangle in the context of this problem as we need to show the relationship between side lengths.

Answer:

Use the distance formula to find the lengths of AB, BC, and AC. Then, substitute the side lengths into the Pythagorean Theorem.