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In geometry, points are called collinear if they all lie on the same line. What, no bunk beds?
Midsegment Theorem 4646 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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