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how to prove that the height of the medial triangle is half of the height of the original triangle????

 Mar 26, 2020
 #1
avatar+632 
+2

Read this article to the end. here

 Mar 26, 2020
 #2
avatar+111321 
+2

 

Let triangle EDF  be  medial, then  AE  = EC   and  that  BD = DC

So....ED splits the sides  AC and BC  in the same proportion  1 : 1

So .....it is parallel to AB.....

And  since  AE  =(1/2) AC  and  BD  = (1/2) BC.....then  ED  =(1/2) AB

 

 

And  by the  same reasoning, we  can show that  EF  =(1/2)BC and FD = (1/2) AC.....then triangles  ABC and DEF are similar figures......and similar figures are  similar in all respects.....so altitude of  medial triangle DEF  = (1/2) altitude of triangle ABC

 

cool cool cool

 Mar 26, 2020
 #3
avatar+632 
+1

Coolio!

AnExtremelyLongName  Mar 26, 2020
 #4
avatar+1956 
-1

Awesome Chris!

CalTheGreat  Mar 26, 2020
 #5
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Thank you! :)

 Mar 26, 2020

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