Mathematics
In figure (2) given below, DE is drawn parallel to the diagonal AC of the quadrilateral ABCD to meet BC produced at point E. Prove that area of quad. ABCD = area of ∆ABE.
Theorems on Area
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Answer
We know that, ∆ACE and ∆ADC are on the same base AC and between the same parallel lines AC and DE.
Area of ∆ACE = Area of ∆ADC
Now, adding ar (∆ABC) on both sides, we get
⇒ Area of ∆ACE + Area of ∆ABC = Area of ∆ADC + Area of ∆ABC
⇒ Area of ∆ABE = Area of quad. ABCD
Hence, proved that area of quad. ABCD = area of ∆ABE.
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