Two parallelograms ABCD and ABEF stand on the same base AB on the same side, between the same parallels. A student says ar(ADF) must equal ar(BCE). Which fact best justifies comparing these by the same-base idea?

Question

Accepted Answer

ar(ABCD) = ar(ABEF), and both contain triangle on AB. Since the two parallelograms on the same base between the same parallels are equal in area, removing the common region leaves equal leftover triangles ar(ADF) = ar(BCE).

Two parallelograms ABCD and ABEF stand on the same base AB on the same side, between the same parallels. A student says ar(ADF) must equal ar(BCE). Which fact best justifies comparing these by the same-base idea?

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