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If the diagonals of a parallelogram are equal, show that is a rectangle

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AC= BD (GIVEN, diagonals of parallelogram as equal)
CD= DC ( common)
AD= BC ( opposite sides of a parallelogram are equal)
ΔACD ≡ ( congurent) ΔBDC ( SSS congruence)
So, angle D = angle C ( corresponding parts of congruent triangles)
ANGLE D + ANGLE C = 180 degrees( co- interior angles)
AS, angle D = angle C  
 
180/2 = 90 degrees
As angle D = C = 90 degrees 
SO, Angle A = C = 90 degrees ( opposite angles of a parallelogram are equal)
AND, B= D = 90 degrees ( opposite angles of a parallelogram are equal)

Posted by

Satyajeet Kumar

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