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Proving Relationships of Parallel and Perpendicular Lines

Proving Relationships of Parallel and Perpendicular Lines 1.13 - Solution

arrow_back Return to Proving Relationships of Parallel and Perpendicular Lines

Let's draw the triangle.

We see that and are acute angles. Therefore, their are not right angles. To determine whether is a right angle, we will calculate the slopes of and If these segments are perpendicular to each other, we know that the triangle is a right triangle.

Side Points Slope
Let's multiply the obtained slopes to see if their product is If this happens, then they are opposite reciprocals and therefore the segments are perpendicular.
Since the product of the slopes is not the segments are not perpendicular. Therefore, the angle they form is not a right angle. This means that the triangle is not a right triangle.