Question

Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 4 and a horizontal side of 10. The other triangle has a vertical side of 12 and a horizontal side of 30. Could the hypotenuses of these two triangles lie along the same line?

Answer 1

For the hypotenuses to be able to lie on the same line:

The tan of angle in both should be the same. That is the two triangles should be similar.

For the first triangle  tanθ  = 4/10 = 2/5

For the second triangle,  tanθ  = 12/30 = 6/15 = 2/5

Since both angles in the triangle are the same, hence, the hypotenuses of the two triangles could lie along the same line.