Question

ഉപകരണങ്ങൾ ഓൺലൈനിൽ

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

Answer 1

Answer:

Explanation:

Given: In parallelogram ABCD, AC=BD

Proof : in △ACB and △BDA

AC=BD  ∣ Given

AB=BA ∣ Common

BC=AD ∣ Opposite sides of the parallelogram ABCD

△ACB ≅△BDA∣SSS Rule

∴∠ABC=∠BAD...(1) CPCT

Again AD ∥ ∣ Opposite sides of parallelogram ABCD

AD ∥BC and the traversal AB intersects them.

∴∠BAD+∠ABC=$180^{0}$

 ...(2) _ Sum of consecutive interior angles on the same side of the transversal is

$180^{0}$

From (1) and (2) ,

∠BAD=∠ABC=$90^{0}$  

∴∠A=$90^{0}$  

 and ∠C=$90^{0}$  

 

Parallelogram ABCD is a rectangle.

Answer 2

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