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?A. The slope of HI is 1/2.B. The slope of EF is 1/2.C. The slope of GH is –2.C. The slope of DF is –2.
Accepted Solution
A:
The order of the letters is very important when we explain the congruence of two triangles.
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 [tex]\overline{DE}[/tex] and [tex]\overline{EF}[/tex] 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.