**Proof:**

Let's consider the given rhombus ABCD.

**1. Diagonal AC bisects angle A:**

To prove that diagonal AC bisects angle A, we need to show that angle DAC is equal to angle CAB.

We know that in a rhombus, all sides are congruent, so AB = BC = CD = DA.

Now, let's consider triangle ABC. Since AB = BC, and angle ABC is a common angle, by the Side-Angle-Side (SAS) congruence criterion, triangle ABC is isosceles.

In an isosceles triangle, the angles opposite the congruent sides are also congruent. Therefore, angle ABC = angle BCA.

Since triangle ABC is isosceles, we can also conclude that angle CAB = angle CBA.

Now, let's consider triangle ADC. Since AD = DC, and angle ADC is a common angle, by the Side-Angle-Side (SAS) congruence criterion, triangle ADC is isosceles.

In an isosceles triangle, the angles opposite the congruent sides are also congruent. Therefore, angle ADC = angle ACD.

Since we know that angle CAB = angle CBA, and angle ADC = angle ACD, we can conclude that angle CAB + angle ADC = angle CBA + angle ACD.

Simplifying, we have angle DAC = angle CAB, which means that diagonal AC bisects angle A.

**2. Diagonal AC bisects angle C:**

To prove that diagonal AC bisects angle C, we need to show that angle BCA is equal to angle ACD.

We have already shown that angle BCA = angle CAB.

Now, let's consider triangle ADC. Since AD = DC, and angle ADC is a common angle, by the Side-Angle-Side (SAS) congruence criterion, triangle ADC is isosceles.

In an isosceles triangle, the angles opposite the congruent sides are also congruent. Therefore, angle ADC = angle ACD.

Since we know that angle BCA = angle CAB, and angle ADC = angle ACD, we can conclude that angle BCA + angle ADC = angle CAB + angle ACD.

Simplifying, we have angle BCA = angle ACD, which means that diagonal AC bisects angle C.

**3. Diagonal BD bisects angle B:**

To prove that diagonal BD bisects angle B, we need to show that angle DBC is equal to angle BCD.

Let's consider triangle ABC. Since AB = BC, and angle ABC is a common angle, by the Side-Angle-Side (SAS) congruence criterion, triangle ABC is isosceles.

In an isosceles triangle, the angles opposite the congruent sides are also congruent. Therefore, angle ABC = angle BCA.

Now, let's consider triangle BCD. Since BC = CD, and angle BCD is a common angle, by the Side-Angle-Side (SAS) congruence criterion, triangle BCD is isosceles.

In an isosceles triangle, the angles opposite the congruent sides are also congruent. Therefore, angle BCD = angle BDC.

Since we know that angle ABC = angle BCA, and angle BCD = angle BDC