Parallelogram on same base and between same parallels have equal area

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GEOMETRICAL VERIFICATION:

GIVEN :

AB ∥ FC and AB is the same base.

Parallelograms ABCD and ABEF are

on the same base AB and between

same parallels AB and FC.

PROOF :

Δ BCE ≅ Δ ADF (By SAS Congruence Criterion)

ar (BCE) = ar (ADF) = =

( Areas of Congruent figures are equal )

OBSERVATION / RESULT / OUTCOME :

Area of the parallelogram ABCD

= Area of the Trapezium ABED + Area of the Triangle BCE

ar (ABCD) = ar (BCE) + ar (ABED)

= + =

Area of the parallelogram ABEF

= Area of the Trapezium ABED + Area of the Triangle ADF

ar (ABEF) = ar (ABED) + ar (ADF)

= + =

Hence the theorem is verified.

Evaluation at the end of the activity

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