Geometric sequences are characterized by having a common ratio, r. It is calculated by getting the ratio of a(n+1) and a(n). We can determine which is the geometric sequence, if we calculate which sequence will have a common ratio. We do as follows:
In any rhombus, the four sides are the same length.
Because of this, we know that
AD = AB
CD = BC
Furthermore, AC = AC due to the reflective property
Those three facts then allow us to prove triangle ACD is congruent to triangle ACB through the SSS congruence property. Then from CPCTC, we then know that angle DAC = angle BAC, which is enough to show that AC bisects the angle shown. The term "bisect" means "cut in half".
