Prove that, any rectangle is a cyclic quadrilateral
Chapter 3 – Circle – Text Book Solution
Practice Set 3.4 | Q 5 | Page 73
Prove that, any rectangle is a cyclic quadrilateral
Given: ▢ABCD is a rectangle.
To prove: ▢ABCD is a cyclic quadrilateral
Proof:
▢ABCD is a rectangle. ....[Given]
∴ ∠A = ∠B = ∠C = ∠D = 90° ....[Angles of a rectangle]
Now, ∠A + ∠C = 90° + 90°
∴ ∠A + ∠C = 180°
We know, if a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic.
∴ ▢ABCD is a cyclic quadrilateral ......[Converse of cyclic quadrilateral theorem]
So, any rectangle is a cyclic quadrilateral.
Explanation:-
Given: ▢ABCD is a rectangle.
To prove: ▢ABCD is a cyclic quadrilateral
Proof:
▢ABCD is a rectangle. ….[Given] Therefore, the angles of the rectangle satisfy: ∠A = ∠B = ∠C = ∠D = 90° ….[Angles of a rectangle]
Now, ∠A + ∠C = 90° + 90° Therefore, ∠A + ∠C = 180°
We know that if a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic.
Therefore, ▢ABCD is a cyclic quadrilateral ….[Converse of cyclic quadrilateral theorem]
Hence, any rectangle is a cyclic quadrilateral.
Chapter 3 – Circle – Text Book Solution
Practice set 3.4 | Q 5 | Page 73
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