The diagonal AC divides the trapezoid ABCD into two similar triangles ABC and ACD, BC = 8cm
| August 19, 2021 | education
The diagonal AC divides the trapezoid ABCD into two similar triangles ABC and ACD, BC = 8cm, AD = 18cm. Find the length of the diagonal AC
By condition, the AC diagonal divides the trapezoid into two similar triangles.
Triangle ABC ~ ACD.
The angle АСD is equal to the angle СD as criss-crossing angles at the intersection of parallel lines ВС and АD of the secant АС. The angle D of the triangle CAD cannot be equal to the angle B of the triangle ABC, then the angle ABC = ACD, and the angle BAC = ADC.
Then in similar triangles ABC and ACD BC / AC = AC / AD = AB / CD.
AC ^ 2 = BC * AD = 8 * 18 = 144.
AC = 12 cm.
Answer: The length of the AC diagonal is 12 cm.
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