Question

Part B:Use the ratios of the side lengths of triangle ABE and triangle BCD to explain your answer to Part A.

Answer 1

The slope of a segment is equal to the ratio of the corresponding vertical side of the triangle to the horizontal side of the triangle.

For the segment AB, the slope is:

$\frac{BE}{AE}$

For the segment BC, the slope is:

$\frac{CD}{BD}$

Since the triangles ABE and BCD are similar, then the ratio of corresponding sides of those triangles are the same. Then:

$\frac{BE}{AE}=\frac{CD}{BD}$

Which means that the slope of both segments is the same.