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### Course: Geometry (FL B.E.S.T.)>Unit 6

Lesson 5: Proving relationships using similarity

# Exploring medial triangles

The three midsegments (segments joining the midpoints of the sides) of a triangle form a medial triangle. Find out the properties of the midsegments, the medial triangle and the other 3 triangles formed in this way. Created by Sal Khan.

## Want to join the conversation?

• I did this problem using a theorem known as the midpoint theorem,which states that "the line segment joining the midpoint of any 2 sides of a triangle is parallel to the 3rd side and equal to half of it."
• There is a separate theorem called mid-point theorem. But it is actually nothing but similarity.
• Couldn't you just keep drawing out triangles over and over again like the Koch snowflake? Wouldn't it be fractal?
• Yes. A type of triangle like that is the Sierpinski Triangle.
• What is SAS similarity and what does it stand for? He mentioned it at ?
• Actually in similarity the ∆s are not congruent to each other but their sides are in proportion to
each other and angles correspond to each other .
Suppose we have ∆ABC and ∆PQR.
AB/PQ = BC/QR = AC/PR and angle A =angle P,angle B = angle Q and angle C = angle R.
Like congruency there are also test to prove that the ∆s are similar. For example SAS ,SSS, AA.
In SAS Similarity the two sides are in equal ratio and one angle is equal to another.
• why do his arrows look like smiley faces? lol
• Yes they do, don't they? lol
• it looks like the triangle is an equilateral triangle, so it makes 4 smaller equilateral triangles, but can you do the same to isoclines triangles?
• Yes, you could do that. Your starting triangle does not need to be equilateral or even isosceles, but you should be able to find the medial triangle for pretty much any triangle ABC. You can either believe me or you can look at the video again. While the original triangle in the video might look a bit like an equilateral triangle, it really is just a representative drawing. In the beginning of the video nothing is known or assumed about ABC, other than that it is a triangle, and consequently the conclusions drawn later on simply depend on ABC being a polygon with three vertices and three sides (i.e. some kind of triangle).
• what does that Medial Triangle look like to you?
• Yeah, Except it's missing the Elder's Wand and the Resurrection Stone is Triangle instead of a Circle (P.S. Dell Dell Cat... I'm a Ravenclaw 2, My Patronus is Also a Lynx, like Kingsley Shacklebolt's:)
• Do medial triangles count as fractals because you can always continue the pattern?
• Medial triangles are considered as fractials because there is always most certianly going to be a pattern
• Can Sal please make a video for the Triangle Midsegment Theorem? I'm really stuck on it and there's no video on here that quite matches up what I'm struggling with.