Triangle DEF is congruent to right triangle GHI with a right angle at vertex H. If the slope of DE is –2, what must be true?

The slope of HI is 1/2

The slope of EF is 1/2

Solution:

Given that,

Triangle DEF is congruent to right triangle GHI

Which means,

These pairs of angles are congruent

{D, G}, {E, H}, and {F, I}

In triangle DEF, E is a right angle

This means that the line segments are perpendicular.

We know that,

Product of slope of a line and slope of line perpendicular to that line is equal to -1

Given that,

Slope of DE = -2

Since the sides EF and HI are congruent,

Slopes of parallel lines are equal

Thus, Slope of HI is 1/2

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