In trapezoid ABCD AD and BC-base, O-point of intersection of diagonals. The areas of triangles AOD and
| August 16, 2021 | education
In trapezoid ABCD AD and BC-base, O-point of intersection of diagonals. The areas of triangles AOD and BOC are 9: 4. Find the ratio of the areas of triangles ABD and CBD
The AOD triangle is similar to the BOC triangle in two angles, since the AOD = BOC angle as vertical angles, the BCO = ADB angle as criss-crossing angles at the intersection of parallel secant lines.
The ratio of the areas of similar triangles is equal to the square of the similarity coefficient, then
K ^ 2 = 4/9.
K = 2/3.
Then BC / AD = 2/3.
In triangles ABD and CBD, the total height BH, then the ratio of the areas of these triangles is equal to the ratio of the lengths of their bases.
Svd / Ssvd = ВС / АD = 2/3.
Answer: The ratio of the areas of triangles ABD and CBD is 2/3.
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