Prove that the sum of the diagonals of a trapezoid is greater than the sum of its bases.
July 22, 2021 | education
| Consider triangles AOD and BCO formed by intersecting diagonals and trapezoid bases.
Because each side of a triangle is less than the sum of the other two sides, then:
AD <AO + OD (for triangle AOD) and BC <BO + OC (for triangle BCO).
Let us add up the inequalities.
AD + BC <AO + OD + BO + OC;
AD + BC <(AO + OC) + (OD + BO);
AD + BC <AC + BD.
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