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?
2 answers:
The order of the letters is very important when we explain the congruence of two triangles.
<span>Triangle DEF is congruent to right triangle GHI means that the following pairs of angles are congruent:
{D, G}, {E, H}, and {F, I}, according to the order of the letters. Thus, in triangle DEF, E is a right angle.
This means that the line segments </span>
and 
are perpendicular.
As we know that the product of the slopes of 2 perpendicular lines (or line segments) is -1, and since the slope of the side DE is -2, then the slope of the side EF must be -1/(-2)=1/2.
Since the sides EF and HI are congruent according to our discussion above, then, the slope of the side HI is also 1/2.
Answer: A and B
<span>Triangle DEF is congruent to right triangle GHI means that the following pairs of angles are congruent:
{D, G}, {E, H}, and {F, I}, according to the order of the letters. Thus, in triangle DEF, E is a right angle.
This means that the line segments </span>
As we know that the product of the slopes of 2 perpendicular lines (or line segments) is -1, and since the slope of the side DE is -2, then the slope of the side EF must be -1/(-2)=1/2.
Since the sides EF and HI are congruent according to our discussion above, then, the slope of the side HI is also 1/2.
Answer: A and B
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