Question

In the figure, ABCD is a quadrilateral. A line through D parallel to AC meets BC produced at E. Prove that ar(∆ABE) = ar. quadrilateral (ABCD)

Answer 1

hey
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given
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ABCD is a quadrilateral

to prove
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ar(∆ABE) = ar (quad ABCD)

proof
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ar(∆ACD)= ar(∆ACE)

•both the triangles are on same base AC and between same parallels AC and DE

adding ar (∆ABC) on both sides

ar(∆ABC) + ar(∆ACD) = ar(∆ABC) +ar(∆ACE)

•ar(quad ABCD) = ar (∆ABE)

prooved

for the diagram refer to the attachment

hope helped
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Answer 2

hey there
refer to attachment