Determine whether the figure is a right triangle. a right triangle contains one 90 degree angle. Justify your answer with slopes. ( question 16)
Answer (2)
If the slopes of two lines are opposite reciprocals of each other, then the lines are perpendicular. This means the angles formed are 90°. To prove this triangle is a right triangle, the opposite and adjacent side must have opposite reciprocal slopes.
Opposite Side: m = x 2 − x 1 y 2 − y 1 m = − 2 + 5 − 3 − 1 m = − 3 4
Adjacent Side: m = x 2 − x 1 y 2 − y 1 m = − 2 − 4 − 3 − 2 m = − 6 5
Since their slopes are not opposite reciprocals, we know that this is not a right triangle .
To determine if a triangle is a right triangle, calculate the slopes of the sides. If the slopes of any two sides are negative reciprocals, the triangle is a right triangle. This confirms that one of the angles is 90 degrees.
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