Question

prove that a cyclic Parallelogram is a rectangle​

Answer 1

Step-by-step explanation:

ABCD is a cyclic parallelogram.

To prove,

ABCD is a rectangle.

Proof:

∠1+∠2=180° ...Opposite angles of a cyclic parallelogram

Also, Opposite angles of a cyclic parallelogram are equal.

Thus,

∠1=∠2

⇒∠1+∠1=180°

1=90°

One of the interior angle of the parallelogram is right angled. Thus,

ABCD is a rectangle.

Answer 2

Answer

Let ABCD be a cyclic quadrilateral such that its diagonals AC and BD are the diameters of the circle  

through the vertices A, B, C, and D.  

As, AC is a diameter and angle in a semi-circle is a right angle

 

⇒∠ADC = 900 and ∠ABC = 900

 

Similarly,  

BD is a diameter.  

⇒∠BCD = 900 and ∠BAD = 900

Thus, ABCD is a rectangle