Question

If the diagonals of a gm are equal then prove that it is rectangle

Answer 1

let ABCD is a parallelogram and its diagonals AC and BD are equal. we have to Congruent ABC triangle and BCD Triangle.
in ABC triangle and BCD triangle we have ,
AB=CD (parallelogram oppsite sides are equal)
BC is the common side .
AC = BD (given )
$\: \: \: \: \: \: \: \: \:$
so ABC triangle is congruent to BCD Triangle so angle b is equal to angle C (by cpct )
AB is parallel to CD and BC is the transversal
so
Angle B + angle C is equal to 180 degree
Angle B + angle B = 180 degree
2 of angle b is equal to 180 degree
so angle b is equal to 90 degree
similarly we can prove all the angle mean angle A, Angle B, angle C and angle d is equal to 90 degree .
so ABCD is a parallelogram having all the angles 90 degree so it is a rectangle .