The height of the isosceles trapezoid drawn from the vertex C divides the base AD into segments of length 2 and 9. Find the length of the base BC.
Take an isosceles trapezoid ABCD with bases AD and BC, | AD | > | BC |, and sides AB and CD, | AB | = | CD |.
In isosceles trapezoid ABCD, draw the heights BM and CN from vertices B and C to the lower base AD. By the condition of the problem:
| AN | = 9;
| ND | = 2;
Based on the properties of an isosceles trapezoid:
| AM | = | ND | = 2;
| BC | = | MN |;
| AM | + | MN | = | AN |;
| MN | = | AN | – | AM | = | AN | – | ND |;
| MN | = 9 – 2 = 7;
As a result, we get for the base BC:
| BC | = | MN | = 7;
Answer: BC base length is 7
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