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Let the vertices of the triangle be $\"\"$ , $\"\"$ , and $\"\"$ .

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Each two vertices form a line segment.

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Find the slopes of three sides of the triangle.

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The formula for slope is $\"\"$ .

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Find the slope of $\"\"$ .

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Substitute $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Find the slope of $\"\"$ .

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Substitute $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the slope of $\"\"$ .

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Substitute $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Observe the three side slopes are $\"\"$ , $\"\"$ , and $\"\"$ .

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Perpendicular lines slopes are negative reciprocals to each other.

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Therefore, the sides of the triangle $\"\"$ and $\"\"$ are perpendicular.

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Perpendicular lines intersect at right angles to one another.

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$\"\"$ is a right angle triangle.

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Thus, $\"\"$ , $\"\"$ , and $\"\"$ are vertices of right triangle.

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$\"\"$ , $\"\"$ , and $\"\"$ are vertices of right triangle.