Question

if the diagonals of parallelogram are equal then show that it is a rectangle​

Answer 1

In triangle ACD and triangle BDC

AC=BD (GIVEN)

DC=DC (COMMON)

AD=BC (OPPOSITE SIDES OF PARALLELOGRAM)

Therefore,triangle ACD is congruent to triangle BDC

Angle D=Angle C (CPCT)

In parallelogram the sum of adjacent angle is 180

therefore angle D+angleC=180

2 angleC=180

Angle C=180/2

Angle C =90

Therefore all angles are of 90 degree

Therefore it is a parallelogram

Answer 2

Answer:

hi!!!!

here is your answer!!!!!!!!!

Step-by-step explanation:

In ΔACD and ΔBDC

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)

all angle are 90 degree.

hence it is rectangle

hope this would help you!!!!!

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