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Midsegment Theorem, a la Shmoop.

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Curious Jorge is competing in the annual ABC triangular jungle gym race for the first time.

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The fastest monkey gets a lifetime supply of bananas.

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Unfortunately, Jorge is the youngest monkey in the 13-18 age category,

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so he can't rely on sheer speed to win.

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He might be able to give himself a leg up if he can

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figure out the length of each section of jungle gym...

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AC is 16 feet, AB is 18 feet, and BC is 6 feet.

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D is the midpoint of AC and E is the midpoint of AB.

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What is the length of DE?

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Well, to figure this out, we can use something called the midsegment theorem.

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The midsegment theorem tells us that, in a triangle...

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...the segment joining the midpoints

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of any two sides will be parallel to the third side and half its length.

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In this case, DE is a segment joining the midpoints of any two sides.

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Therefore, by the midsegment theorem, DE is parallel to BC,

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and is half its length, so we can write DE equals half BC.

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Since BC is 6, we can substitute 6 into the formula, multiply it by ½,

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and get the length of DE, which is 3 feet.

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As it turns out, all of the older monkeys

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exert themselves too much early on and are wiped out for the home stretch...

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...while Jorge has paced himself perfectly, and winds up the top banana!

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