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Midsegment Theorem 4644 Views


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Description:

Who knew triangles had midsegments? We did.

Language:
English Language

Transcript

00:05

Midsegment Theorem, a la Shmoop.

00:08

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

00:14

The fastest monkey gets a lifetime supply of bananas.

00:18

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

00:23

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

00:25

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

00:28

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

00:33

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

00:40

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

00:45

What is the length of DE?

00:49

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

00:53

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

00:56

...the segment joining the midpoints

00:58

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

01:02

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

01:06

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

01:11

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

01:16

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

01:23

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

01:26

As it turns out, all of the older monkeys

01:28

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

01:35

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

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