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△DEF and △FGH similar right triangles. The coordinates of all the vertices are integers. The relationship between the slope of DF¯¯¯¯¯ and the slope of FH¯¯¯¯¯¯ cannot be determined, because the triangles are congruent. The slope of DF¯¯¯¯¯ is less than the slope of FH¯¯¯¯¯¯ . This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for DF¯¯¯¯¯ than for FH¯¯¯¯¯¯ . The slope of DF¯¯¯¯¯ is equal to the slope of FH¯¯¯¯¯¯ . This this because ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for DF¯¯¯¯¯ as for FH¯¯¯¯¯¯ The slope of DF¯¯¯¯¯ is greater than the slope of FH¯¯¯¯¯¯ . This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for DF¯¯¯¯¯ than for FH¯¯¯¯¯¯ .

Congruent triangles are triangles with the same sides and the same measure of angles. You are given triangle DEF which is similar to triangle FGH. From the figure, side FH is larger than side DF. So the statement of them being congruent cancels out. Triangle DEF is smaller in size than triangle FGH. So they are not congruent. The slope is defined as the rise overrun. Side DF has the same slope as side FH. Sides DE and FE are proportional to sides FG and HG. Only C and D are correct.

Step-by-step explanation: