Question

Vinnie wants to use two similar triangles,
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D
E
F
and
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P
Q
R
, to show that the slope of a line is the same between any two points on that line. Which of the following representations BEST demonstrates what Vinnie wants to show?


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Answer 1

I can’t see the four images you pasted — could you re-upload them or tell me which one shows which picture? Meanwhile, here is how to tell which diagram is correct and why:

The best diagram is the one that shows two triangles whose hypotenuses lie on the same straight line and whose legs are horizontal and vertical (so each triangle is a right triangle with the same acute angle where the hypotenuse meets the horizontal). In that picture the triangles are similar by AA (they share the acute angle formed with the line, and each has a right angle). Because the triangles are similar, corresponding side ratios are equal, so

rise/run for the large triangle = rise/run for the small triangle.

That equality is exactly the statement that the slope (rise over run) is the same between any two points on the line.

So pick the option that:
- Places both triangles along the same line (their hypotenuses coincide with that line),
- Makes the vertical legs parallel to each other and the horizontal legs parallel to each other (i.e., forms two right triangles with the same acute angle).

If you upload the four images I’ll point to the exact choice.