Question

PLEASE HELP!!!!

Which characteristics will prove that triangle DEF is a right, scalene triangle?


A. DE, EF, and DF are all different lengths, and their slopes are the same.


B. DE, EF, and DF are all different lengths, and the slopes of DE and EF opposite reciprocals.

Answer 1

B. DE, EF, and DF are all different lengths, and the slopes of DE and EF opposite reciprocals.

Explanation:

I took the test and the answer was B

Answer 2

Options

• 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.

Answer:

(B) DE, EF, and DF are all different lengths, and the slopes of DE and EF opposite reciprocals.

Explanation:

Given a triangle DEF

To prove that it is a right scalene triangle, we must show that two of its sides are perpendicular. This is done by showing that the slopes of two adjacent sides are opposite reciprocals.

In a scalene triangle, no side length is equal to another. Therefore, all the sides DE, EF, and DF are not equal in length.

The correct option is B.