The sides of the trapezoid are 3 cm and 4 cm, and the bases are 5 cm and 10 cm.
| February 2, 2021 | education
The sides of the trapezoid are 3 cm and 4 cm, and the bases are 5 cm and 10 cm. At what angle do the extensions of the lateral sides of the trapezoid intersect?
In the AED triangle formed by the extension of the lateral sides, the BC segment is its midline, since the base of AD is twice as large as the BC segment. Then the length of the segment BE = AB = 3 cm, the length of the segment EC = СD = 5 cm. In a triangle ВЕС, the lengths of the sides are 3 cm, 4 cm, 5 cm, which is an “Egyptian” triangle.
Then the angle BEC = 90. Let’s check it by the Pythagorean theorem.
5 ^ 2 = 25.
(3 ^ 2 + 4 ^ 2) = 9 + 16 = 25.
Answer: When extending the sides, they intersect at right angles.
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