Question 1062306: I have three questions to ask. Both are inter-related I think.
1. Will three altitudes determine a triangle? Why?
2. Will three medians determine a triangle? Why?
3. How can I draw a triangles when only three altitudes are given? I already found how I can draw it using medians.
I want a concrete proof for both of them. Sorry for my english if there are any mistakes. I'm not a native english speaker.
Answer by ikleyn(53765)   (Show Source):
You can put this solution on YOUR website! .
Regarding your questions #1 and #3, see these links
http://www.cut-the-knot.org/triangle/tr3.shtml
https://answers.yahoo.com/question/index?qid=20110520005044AAQiQMO
See also the book "The secrets of Triangles" by Posamentier and Lehmann, 2012, ISBN 978-1-61614-587-3, Example 14, p. 238.
Regarding your question #2, see this link
http://www.qc.edu.hk/math/Junior%20Secondary/Median.htm
and also the same book, Example 17, p. 247.
You can search for this book in your local library.
Also, you have this free of charge online textbook on Geometry
- GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
In this online textbook, there are lessons on basic construction procedures in Geometry under these topics:
Geometric constructions using a compass and a ruler. Basic operations
Geometric constructions related to parallel lines
Geometric constructions related to circles
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