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Use coordinates to prove geometric theorems algebraically Videos 3 videos
One formula to rule them all, one formula to find them. One formula to bring them all, and in the darkness bind them. Or something like that. I...
Coordinate geometry isn't your average geometry. Check out the video to find out why.
Midsegment Theorem 4647 Views
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Description:
Who knew triangles had midsegments? We did.
- Plane Geometry / Plane figures (triangles, rectangles, parallelograms, trapezoids, circles, polygons)
- Mathematics and Statistics Assessment / Plane Geometry
- Geometry / Use coordinates to prove simple geometric theorems algebraically
- Properties, Measurement, and Dimension / Use coordinates to prove geometric theorems algebraically
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.
Full Transcript
- 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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