SOLUTION: Please help me to prove this problem Given triangle HNS,O is the midpoint of HN,E is the midpoint of NS Prove OE parallel to HS,OE one half HS

Algebra ->  Geometry-proofs -> SOLUTION: Please help me to prove this problem Given triangle HNS,O is the midpoint of HN,E is the midpoint of NS Prove OE parallel to HS,OE one half HS       Log On


   

Question 1104993: Please help me to prove this problem Given triangle HNS,O is the midpoint of HN,E is the midpoint of NS Prove OE parallel to HS,OE one half HS
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
(1/2) = ON/HN = EN/SN with angle SNH common to both triangles
:
therefore triangles HNS and ONE are similar, therefore
:
OE/HS = 1/2 iff 2*OE = HS
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OE is parallel to HS since similar triangles have the same angles, that is, angle SHN = angle EON
:

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
See the lesson
    - The line segment joining the midpoints of two sides of a triangle
in this site.

In the systematic and consistent/coherent course of Geometry, this statement (this Theorem) is preceding (far preceding) the similarity theory.


In this site, you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK

The referred lessons are the part of this online textbook under the topic  "".


Save the link to this online textbook together with its description

Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson

to your archive and use it when it is needed.