Hi All,

This DS question is built around the concept of similar triangles, which is a relatively rarity on Test Day (you probably will not see it, and if you do see it, it would likely be just once).

Similar triangles are triangles with the exact same angle measurements, but different side lengths. When dealing with similar triangles, the 'key' to solving for any of the side lengths, the area, the perimeter, etc., is to determine how any pair of equivalent sides relates to one another (e.g. if the 'first side' in the small triangle is exactly a third of the 'first side' in the larger triangle, then THAT relationship will hold true for the other 2 paris of sides).

This question is designed in such a way that you don't have to do any calculations to solve it, as long as you understand the 'rules' involved.

Here, since DE is parallel to AC, Angle A = Angle BDE and Angle C = Angle BED. Thus, we have similar triangles. We're asked for the length of DE.

Fact 1: AC = 14

This Fact is not enough to define the relationship or any other side lengths.

Fact 1 is INSUFFICIENT

Fact 2: BE = EC

This Fact tells us that BE is HALF of BC, which DOES define the relationship, but does NOT give us any values to work with.

Fact 2 is INSUFFICIENT

Combined,

Fact 1 gives us a value

Fact 2 defines the relationship.

Thus, we CAN determine the value of DE (it's half of AC)

Combined, SUFFICIENT

Final Answer:

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Rich

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