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 ...

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 ...

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 ...

Description This model of a part of a hinged dissection consists of two triangles hinged at a common vertex. Objects MA.304723.755, MA.304723.760, and MA.304723.804 form model 6TQ (angle bisectors of ...

The secret to getting ahead is getting started. In the triangle above, segment BD is an angle bisector. Sides AB = 9x − 14, BC = 4x − 3, CD = 2x + 11 and AD = 5x + 2. Find the area of triangle ABD and ...

The four triangular pieces of two models denoted by MA.304723.755 and MA.304723.760 may be arranged to form a parallelogram (in two ways) and a triangle (in two ways), constituting a partially hinged ...