Let
In the triangle BDC we have
In the triangle ADC we have
Then
I have this Geometry problem here which is a proof question.
I am really unsure of where to start, but I have been told by the teacher that using congruent triangles might help, but does that mean I will need to draw in a line onto the diagram? I'm not quite sure where to start.
Thanks.
I wonder if this is the construction that the teacher had in mind. Let E be a point on BC such that angle EDC = angle ADC. Then see if you can prove these facts:
1. Triangles DEC, DAC are congruent.
2. Angle DEC = angle DAC = 2× angle DBE.
3. Triangle BDE is isosceles.
4. BE = DE = DA.
5. BC = BE + EC = AD + AC.