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### Course: Geometry (all content)>Unit 4

Lesson 6: Medians & centroids

# Median, centroid example

Example involving properties of medians. Created by Sal Khan.

## Want to join the conversation?

• for any triangle do you need to use these specific letters to describe them?
• No,choose the smbols that you're comfortable with.
• At I tried to find the length of FH by using the pythagorean theorem, already knowing the length of GH and FG. So GH is 6, as Sal showed, and I thought that CF=AD=15. FG is "the shorter part" of CF, so it should equal 1/3*15=5, shouldn't it? Now the problem occurs: according to pythagorean theorem, FG^2=GH^2+FH^2 and this is equal to 5^2=6^2+2^2 ! Where did I go wrong...?
• The median lines aren't necessarily all the same length. You can't assume `CF=AD`.
• @ is Sal making an assumption that AG is the longest part ?
• He may be eyeballing it, but you can also tell by the fact that line AG goes all the way past point F on its side, which is also the point that bisects line AE. That shows that AG is longer by proportion than line GD, or the longer part of the median if that made sense :)
• Around , he says that the area of all the smaller triangles are 18, and we know that the longer leg is also 18. Is just a coincidence?
At , he writes that AF, and HE, both equal 6, but AE equals 12, leaving no room for FH, at , he says that FH is equal to 2. But Af(6), HE(6), and FH(2), does not equal AE(12).
Why is that?
• Yeah, it is just a coincidence.

He actually does not say that HE = 6, he says that FE = 6 and FH = 2 and 6-2 = 4 so really HE = 4. The total is 6 + 2 + 4 = 12. Hope that helps!
• Why is there so many different way's to solve this problem? Wouldn't it be a lot easer if there was just one way to solve it?
• Actually, this is the <b>magical part<b> of mathematics, there are so many ways to prove a single proposition, and all of them are authentic.
Let's suppose that you are willing to meet your friend Alex. And you have 4 options to reach him:
1. You can reach there by foot,
2. Take a taxi
3. Take your own car, (if you have one)
4. Take the bus if available.
see, all these options are legitimate and will take you to your destination. so happy journey.
(1 vote)
• Is angle AEB 45*?
• No a median doesn't necessarily bisect the angle.
Also look at <HEG which is the same measure as AEB.
Point G is 4 above and 6 to the right of point E, if it was 45 degrees those two distances would have to be the same and they are not.
• Do you need to divide by six?
• How could you know that the triangles are similar?
(1 vote)
• @Rita:
it is wrong because 1. You cannot prove triangles similar by proofs (ASA, AAS, etc); proofs prove triangle congruence. 2. AAA is not a form of triangle congruence.
the two triangles are similar because Sal states that the hypotenuse of triangle AHG (10) is 2/3 of the length of the hypotenuse of triangle AED (15). Same with their bases; HG (6) is 2/3 of the length of HG (9). The same can also be said for their heights; AH (8) is again 2/3 of the length of AE (12). :)