Question

E is the mid-point of the non-
parallel side BC of a trapezium ABCD. E is joined to the opposite vertices A and D. Prove that triangle ABE + triangle DCE = 1/2 trapezium ABCD.
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Answer 1

Answer:

given : ABCD is a trapezium . such that AB || DC.

E is the mid-point of BC.

TPT: area(∆ABE)+area(∆DEC)=1/2*area(trapezium ABCD)

proof:

area(∆ABE) = 1/2*area(∆ABC) ..........(1) [since the median divides the triangle into equal parts]

similarly area(∆DEC) = 1/2*area(∆BDC)...........(2)

area(∆BDC)=area(∆ADC) [triangles formed between same pair of parallel lines and with the same base are equal in areas]

therefore area(∆DEC)=1/2*area(∆ADC)......(3)

adding eq(1) and eq(3):

area(∆ABE)+area(∆DEC) = 1/2*[area(∆ABC)+area(∆ADC)]=1/2*area(trapezium ABCD)

Answer 2

Answer:

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