Constructions (accurate drawings) can be made using a ruler, a pair of compasses and a pencil. A line which cuts an angle into two equal side angles is called an angle bisector. In geometry a ...

Summary We prove the next generalization of the Steiner-Lehmus theorem: if two equal cevians intersect with each other on the angle bisector of the third triangle vertex, then the triangle is ...

In the diagram below, AB is the chord of a circle with centre O. OM is perpendicular to AB (meet at a right angle). Look at triangles OAM and OBM. The hypotenuses (OA and OB) are the same, as they are ...

The six intersection points of a triangle’s non-parallel altitudes and perpendicular bisectors are the vertices of two congruent minor periambic triangles which are inversely similar to the original.