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Answer :
Explanation:-
Since triangles KLM and NPQ are similar right triangles, we can use the proportion of their corresponding sides to show that the slope of NP is equal to the slope of KL. The slope is defined as the ratio of the vertical change to the horizontal change between two points.
The proportion that can be used to show that the slope of NP is equal to the slope of KL is the ratio of their corresponding side lengths. Since triangles KLM and NPQ are similar, their corresponding sides are in proportion. Therefore, the proportion that can be used is: NP/KQ = KL/KM where NP and KL represent the slopes of the lines passing through the corresponding sides of the triangles
Step 1: Identify the corresponding sides of the triangles.
Let KM represent the horizontal side of triangle KLM, and ML represent the vertical side. Similarly, let NQ represent the horizontal side of triangle NPQ, and PQ represent the vertical side.
Step 2: Write the proportion using the corresponding sides.
Since the triangles are similar, we have the proportion:
(ML/KM) = (PQ/NQ)
Step 3: Recognize that the proportion represents the slopes of the lines KL and NP.
The slope of KL is the vertical change (ML) divided by the horizontal change (KM), and the slope of NP is the vertical change (PQ) divided by the horizontal change (NQ).
Step 4: Conclude that the slopes of KL and NP are equal.
Based on the proportion, we can conclude that the slope of NP is equal to the slope of KL.
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