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I've been trying to help, but my ipad hates me! (;
To start, know that parallel lines have the same slope, but different y intercepts
I like to use the formula y=mx+b for these types of problems
m is the slope
b is the y interecept
Anyway, since those triangles are similar, the slope of the hypotenuses on each of the triangles should be the same
Ignore the shape of the triangles and pretend that the hypotenuses are two individual lines.
Then you have to find their formulas
I cannot draw on an ipad with openstudy so I have written this summary
The line that makes the hypotenuse of the big triangle has the points (-5,8) and (1,2)
The little triangle's hypotenuse has the points (4,5) and (7,2)
Then I used the slope formula for both, which is m= (y2 - y1)/(x2-x1)
For both triangles I got a slope of -1
I dont know if this is required, but I also proved that the lines are parallel
I rewrote the formulas for both triangles as y=-x+b
For the big triangle, I plugged in a point to solve for b
And got y=-x +3
I did the same for the little triangle and got
y = -x + 9
This proves that the hypotenuses are parallel and have the same slope