In rectangle ABCD AB = 5 cm, BC = 9 cm, BF is the bisector of angle B. Determine the midline of the trapezoid BCDF.

univerkov | September 30, 2021 | education

1. MK – the middle line of the trapezium ВСДF.

2. Bisector BF divides the rectangle into two geometric shapes: triangle ABF and trapezoid BCDF.

3. According to the properties of the rectangle, triangle ABF is isosceles.

Hence, AB = AF = 5 cm.

4. Segment DF = AD – AF.

AD = BC = 9 cm (the sides of the rectangle opposite each other, according to its properties, are equal).

DF = 9 – 5 = 4 cm.

5.MK = (DF + BC) / 2 = (9 + 4): 2 = 6.5 cm.

Answer: MK = 6.5 cm.

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