Question

quadrilateral.
2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.​

Answer 1

Given :

• ABCD is a parallelogram
• Diagonals are equal , i.e. AC = BD

To prove :

• ABCD is a rectangle

Proof :

From the figure ,

In ∆ABC and ∆ ABD ,

• AB = AB (common)
• AC = BD (given)
• AD = BC ( opposite sides of parallelogram are equal)

$\therefore \tt \Delta ABC \cong \Delta ABD$

Hence , ∠ABC = ∠BAD [By CPCT]

Now , we know that the sum of adjacent angles in a parallelogram is 180°

$\therefore$ ∠ABC + ∠BAD = 180°

∠ABC + ∠ABC = 180°

2 ∠ABC = 180°

∠ABC = 180° / 2 = 90°

Since , one angles of the parallelogram is 90° , therefore it is a rectangle .