Question

05.02)

Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 2 and a horizontal side of 6. The other triangle has a vertical side of 10 and a horizontal side of 30.

Could the hypotenuses of these two triangles lie along the same line?

No, because they are not similar triangles
No, because one is larger than the other
Yes, because they are both right triangles
Yes, because they are similar triangles

Answer 1

Yes, because they are similar triangles

Explanation:

I got the answer right on the test

Answer 2

Compare the vertical/horizontal ratios to the slope of a line. In the first triangle the vertical/horizontal ratio (which can also be described as the rise over the run, which is the slope definition) is 2/6 or 1/3. In the second triangle, the vertical/horizontal ratio is 10/30 or 1/3. Both of the third sides have a slope of 1/3, so the answer is the last one.