In the parallelogram ABCD, the diagonal AC is the bisector of angle A, find the side BC if the perimeter of ABCD is 34

1. According to the properties of a parallelogram, the angles located opposite each other are equal.

Therefore, ∠A = ∠C.

2. The bisector AC divides the indicated angles into two equal parts. That is, ∠ВАС = ∠АСВ and ∠САD = ∠АСD.

3. The angles at the bases of triangles ABC and ACD are equal. Therefore, these triangles are isosceles. AB = BC and AD = CD.

4. All sides of a given parallelogram are equal. With this in mind, we calculate the length of each side:

AB = BC = CD = AD = 34: 4 = 8.5 units.

Answer: BC side length = 8.5 units.