In these problems, information is given about a triangle to identify physical attributes. The problem is to describe ruler and compass constructions of the triangle from the given attributes. For consistent notation adapted to this environment I use the following:
The angles at vertices A, B, C: A, B, C
The sides of the triangle opposite vertices A, B, C: a, b, c.
The medians: ma, mb, mc
The altitudes: ha, hb, hc
The segments along an angle bisector to the opposite side: da, db, dc
The radius of the circumcircle: R
The radius of the incircle: r
The radii of the excircles: ra, rb, rc
The notation: b+c will
mean "given a line segment equal in length to the sum of
the lengths of sides b and c.
One Solution (In Microsoft
A GSP Sketch
Another GSP Sketch
2. Triangle given two sides and the median to one of those sides.
a, b, ma
3. Triangle given a side, an altitude to that side and a median to that side.
a, ha, ma
4. Triangle give a side, the altitude to that side and the median to a different side
a, ha, mc
GSP file for demonstration
5. Triangle, given a side, the angle opposite the side, and the radius of the incircle
a, A, r
6. Triangle, given a side and the altitudes to the other two sides.
a, hb, hc
7. Triangle, given a side, an altitude to another side, and the angle bisector to the third side.
a, hb, dc
Click HERE for a GSP Sketch and Script tool
22. Create other triangle construction problems.