If a triangle ABC is classified as a right triangle, which statement is true? (6 points) Group of answer choices

All three angles of triangle ABC are congruent.

Two slopes of triangle ABC are congruent.

All three sides of triangle ABC are congruent.

Two slopes of triangle ABC are opposite reciprocals

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  (d)  Two slopes of triangle ABC are opposite reciprocals

Step-by-step explanation:

If angles or sides of the triangle are congruent, the triangle is equilateral. All angles are 60°, so the triangle is not a right triangle.

No sides of any triangle can ever be parallel, so the slopes of two sides will never be congruent.

Eliminating the impossible answer choices leaves the only one that is (mostly) correct:

  Two slopes of triangle ABC are opposite reciprocals

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Additional comment

When the slopes are opposite reciprocals, the lines are perpendicular. For the triangle to be a right triangle, two sides must be perpendicular (meet at right angles).

The exception is when one side is vertical (has undefined slope). There is no "opposite reciprocal" for "undefined." Hence the statement will be true only if triangle ABC does not have two sides aligned with the coordinate axes.

Two slopes of triangle ABC are opposite reciprocals

Step-by-step explanation:

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