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Triangle KLM and triangle PAS are similar right triangles.

Which proportion can show that the slope of KM is equal to the slope of PS?

Answer :

The proportion that can be used to show that the slope of KM is equal to the slope of PS is:

KL/KP = LM/AS

In similar triangles, corresponding sides are proportional. Since triangle KLM and triangle PAS are similar right triangles, we can use the proportionality of corresponding sides to show that the slope of KM is equal to the slope of PS.

Let KL be corresponding to KP, and LM correspond to AS. Then, the proportion KL/KP = LM/AS can be used to show that the slope of KM is equal to the slope of PS. This is because the slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate.

Therefore, if the ratio of the corresponding sides is the same, then the ratio of the slopes will also be the same.

In this case, since we know that triangle KLM and triangle PAS are similar right triangles, we can use the proportionality of corresponding sides to show that the slope of KM is equal to the slope of PS.

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