Respuesta :
Question:
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.
Answer:
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 [tex]\overline{DE}\ and\ \overline{EF}[/tex] 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
[tex]\text{ Slope of DE } \times \text{ slope of EF} = -1\\\\-2 \times \text{ slope of EF} = -1\\\\\text{ slope of EF} = \frac{1}{2}[/tex]
Since the sides EF and HI are congruent,
Slopes of parallel lines are equal
[tex]Slope\ of\ HI\ = \frac{1}{2}[/tex]
Thus, Slope of HI is 1/2
Answer:
It is A
Step-by-step explanation:
It is right because i got it right on edge.
