Question

7. In Fig. 12.32, ABCD is a trapezium with AD and BC
as parallel sides and Z BAD = 90°. BD and AC cut
at E. Prove that A ABE is equal in area to A CED.
(ICSE)
B
90°
Fig. 12.32​

Answer 1

Answer:

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Answer 2

Answer with Step-by-step explanation:

In trapezium ABCD

Angle BAD=90 degrees

AD is parallel to BC

Theorem: When two triangle lie between same parallel lines and lie on the same base then, the their area are equal.

Triangle ABD and triangle ACD lie on same base AD and formed between same parallel lines AD and BC.Then,

Ar(ABD)=Ar(ACD)

Ar(ABD)-ar(AED)=Ar(ACD)-ar(AED)

Ar(ABE)=Ar(CED)

Hence, proved.

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