Explain why the hypotenuses of the triangles below have the same slope.

The hypotenuse of the two triangles have the same slope because they are in the same straight line and the slope of a straight line is constatn.

You can prove that in this way:

slope = rise / run = Δy / Δx

For the upper triangle: slope = (4 - 2) / (8 - 4) = 2 / 4 = 1 / 2

For the lower triangle: slope = (-1 - (-5)) / (- 2 - (-10)) = 4 / 8 = 1 / 2

So, this proves that the two slopes are the same: 1 / 2