Find the perimeter of parallelogram ABCD if the bisector of angle B divides AD into 6 cm and 4 cm segments.

Let us denote the bisector of the angle ВK
By condition, a parallelogram is given, which means that ВС || AD. ВK – secant, the angle СВK is equal to the angle ВКА, as cross-lying angles
The angle ABK is equal to the angle CBK (BK is the bisector), therefore, the angle ABK is equal to the angle BKA. Consider the triangle ABK, it is isosceles, AB = AK = 6 cm.
AD = 6 + 4 = 10 (cm).
Find the perimeter of the parallelogram:
P = 2 * (a + b) = 2 * (10 + 6) = 2 * 16 = 32 (cm).
Answer: The perimeter of parallelogram ABCD is 32 cm.