Question

if the diagonals of parallelogram are equal than prove that it is a rectangle

Answer 1

Given : A parallelogram ABCD in which AB=CD
To prove: ABCD is a rectangle.
Proof: In tri.ABC and tri.DCB, we have,
AB=CD (Opposite sides of llgm.)
BC=CO (Common)
AC=DB (Given)
By SSS, tri.ABC =~ tri. DCB
By CPCT, ang. ABC= ang. DCB
But AB ll DC and BC cuts them.
Therefore, ang. ABC+ ang. DCB=180
=> 2(ang.ABC)=180
=> ang. ABC=ang. DCB=90
Thus, ABCD is a llgm with 90.
So, ABCD is a rectangle. 'Proved'

Tri. =triangle & ang. =angle
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