The diagonal crosses the middle line of the trapezoid and divides it into 3 cm and 5 cm segments
| September 17, 2021 | education
The diagonal crosses the middle line of the trapezoid and divides it into 3 cm and 5 cm segments. Find the lengths of the bases of the trapezoid.
Consider triangle ACD. Since MK is the middle line of the trapezoid, the OK segment is the middle line of the ACD triangle.
The midline of a triangle is half the length of the base parallel to the midline.
OK = AD / 2.
AD = 2 * OK = 2 * 5 = 10 cm.
Similarly, in the triangle ABC, the MO segment is the middle line, then BC = 2 * MO = 2 * 3 = 6 cm.
Answer: The lengths of the bases of the trapezoid are equal: AD = 10 cm, BC = 6 cm.
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