If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.
You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!
Goal: Construct a triangle given its three medians ta, tb and tc. Base your construction on the definition of the median and the fact that the three medians of a triangle meet at a single point T and T is 2/3 of the way along each of the medians. (T is called the centroid.)
YouTubeMathcastorScreenCast Mathcast (if YT is blocked)
GeoGebra Construction: Watch the C+S construction and then test it Directions for InterActivity
1. Click on Play to see the construction unfold.
2. Select the Move tool and click & drag the endpoints of the three medians.
3. Drag one of the median endpoints "too" small or "too" big. The triangle disappears. Why?
Proof
Now we can ask - when does a triangle exist? We get them to look in detail at Figure 8, that is, at the construction of triangle ATD. This is just a basic C+S construction of a triangle given 3 side lengths. Here the 3 sides have lengths: |AT|=2/3·ta, |AD|=2/3·tb and |TD|=2/3·tc.
The students should know that a triangle exists if and only if the sides satisfy the triangle inequality. We write down one inequalities, e.g. 2/3·ta+ 2/3·tb £ 2/3·tc. They should see that they can multiply by 3/2 and get the inequality: ta+ tb £tc. We have them write down the other 2 analogous inequalities and then have them write the concluding sentence:
A triangle with medians ta+ tb and tcexists and is unique if and only if the 3 medians satisfy the triangle inequality.
Metadata
Global
Advanced Compass and Straightedge Constructions with GeoGebra
Brief
Construction: Construct a triangle given its medians
TOC - Advanced C+S
Play to see the construction unfold.
Move tool and click & drag the endpoints of the three medians. 
Comments (0)
You don't have permission to comment on this page.