Question

IN THE FIGURE 5.24 TO THE RIGHT ABCD IS A RHOMBUS.SHOW THAT AC IS THE BISECTOR OF <BAD.​

Answer 1

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".