Using what we know from Euclidean geometry, PROVE that a triangle is the medial triangle of its anticomplementary triangle. (Make sure to clearly write-out the hypothesis and the conclusion of the
statement.)
PROVE that a triangle is the medial triangle of its anti-complementary
triangle.
Defn medial triangle from mathworld
The triangle
triangle
formed by joining the midpoints of the sides of a
.
Anti-complimentary triangle from mathworld
The anticomplementary triangle is the triangle
triangle
as its medial triangle.
which has a given
PROOF
Note: this follows straight from the definition.
Do you possibly have a different definition for anticomplimentary triangle than that
on Mathworld???
Consider a triangle A1A2A3, as pictured below
let triangle A’1A’2A’3 be it’s anticomplimentary triangle, as shown in above diagram
Then triangle A1A2A3 is the medial triangle of triangle A’1A’2A’3 , by defn. of
anticomplimentary triangle.
In other words, our original triangle is the medial triangle of it’s anticomplimentary
triangle.
#
Note: this was a relatively simple proof – do you possibly have a different definition
than on mathworld??? Check out mathworld to see their defn.