Triangle inequality; medians, altitudes and bisectors
Build a triangle from three sticks and find out which three lengths make a triangle and which don't. Then test a median, an altitude and a perpendicular bisector on a triangle you reshape yourself, and see where the three medians always meet.
- France: grade 7
- Germany: grade 7
- Iran: grade 7
- Afghanistan: grade 7
- Syria: grade 8
- Palestine: grade 6
- Ukraine: grade 7
- Russia: grade 7
Guide
Matches Iran Grade 7 and Afghan Grade 7–8 geometry (relations between segments; medians, altitudes and bisectors); in England the special lines come up with ruler-and-compass constructions in KS3. The coloured dots and hollow rings can be dragged; the readouts under the figure update live.
Three lengths make a triangle only if each one is shorter than the other two added together. If one length is exactly the sum of the other two, the two short sides lie flat along the long one and there is no triangle.
A median joins a vertex to the midpoint of the opposite side. An altitude goes from a vertex at right angles to the opposite side (or that side extended). An angle bisector cuts an angle in half. The perpendicular bisector of a side passes through its midpoint at right angles; it need not pass through a vertex.
To construct the perpendicular bisector and the angle bisector with a compass, see the Constructions studio. Here the lines are already drawn and you test them.