In a trapezoid with a middle line of 20 cm, a straight line is drawn through one of its vertices, parallel to the lateral side
| August 6, 2021 | education
In a trapezoid with a middle line of 20 cm, a straight line is drawn through one of its vertices, parallel to the lateral side and intersecting the middle line in its middle. Find the larger base of the trapezoid.
1. A, B, C, D – the tops of the trapezoid. Midline MK = 20 centimeters. CE – straight line parallel to AB. MO = KO.
2. The geometric figure of AMOE is a parallelogram, so its sides are parallel. Therefore, AE = MO = 10 centimeters.
OK – the middle line of the triangle CDE, as it is part of the middle line of the trapezoid ABCD.
DE = 2KO = 20 centimeters.
3. The larger base of the trapezoid AD = AE + DE = 10 + 20 = 30 centimeters.
Answer: AD – the larger base of the trapezoid is 30 centimeters.
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