Prove segment de is parallel to segment ab

We can compare the slopes of the two segments. Two segments (and two lines in general) are parallel if they have the same slope. The slope is computed as

In this case, we have

and

Since both segments have the same slope, namely 0, they are parallel.

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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