Which characteristics will prove that ΔDEF is a right, scalene triangle? segment DE, segment EF, and segment DF are all different lengths, and their slopes are the same. Segment DE, segment EF, and segment DF are all different lengths, and the slopes of segment DE and segment EF opposite reciprocals. Segment DE, segment EF, and segment DF are all the same length, and their slopes are the same. Segment DE, segment EF, and segment DF are all the same length, and their slopes are opposite reciprocals.

Respuesta :

The correct option is "Segment DE, segment EF, and segment DF are all different lengths, and the slopes of segment DE and segment EF opposite reciprocals".

Scalene Triangle

A scalene triangle is a triangle whose all three sides are of different lengths.

Perpendicular Lines

We know that to show that the two lines are perpendicular their slope must be reciprocal and opposite of each other.

To find

ΔDEF is a right, scalene triangle

Solution

In a right-angled triangle, there must be an angle of 90°, therefore, the line segments should be perpendicular to each other. Thus, the slope of the two-line segments must be reciprocal of each other.

Also, we want that the triangle must be a scalene triangle, and for a triangle to be scalene all the sides of the triangle must be different in length.

Hence, the correct option is "Segment DE, segment EF, and segment DF are all different lengths, and the slopes of segment DE and segment EF opposite reciprocals".

Learn more about Right scalene triangle :

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Answer:

b

Step-by-step explanation: