Question

3.
A
In the given figure, ∆A and ∆D are right angles and
BE = CE. If E is the mi dpoint of AD, show that
AABE = ADCE and prove that AB = DC.



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Answer 1

In △ABC

D is mid point of BC

⇒AD is the median.

similarly In △EBC

D is mid point of BC

⇒ED is median.

As median divides a given triangle

in two triangles of equal area

⇒ar(△ABD)=ar(△ACD) ___(1)

ar(△EBD)=ar(△ECD) __(2)

(1)-(2) statement

ar(△ABD)−ar(△EBD)=ar(△ACD)−ar(△ECD)

⇒ar(△ABE)=ar(△ACE)__(3)

statement (2) and (3) are proof of

part (I) and (II) respectively.