Q: 12     Prove that a cyclic parallelogram is a rectangle.
 

Answers (1)
M mansi

Given: ABCD is a cyclic quadrilateral.

To prove: ABCD is a rectangle.

Proof :

            

  In cyclic quadrilateral ABCD.

            \angle A + \angle C = 180 \degree.......................1(sum of either pair of opposite angles of a cyclic quadrilateral)

           \angle A = \angle C........................................2(opposite angles of a parallelogram are equal )

        From 1 and 2,

        \angle A + \angle A = 180 \degree

  \Rightarrow 2\angle A = 180 \degree

 \Rightarrow \angle A = 90 \degree

We know that a parallelogram with one angle right angle is a rectangle.

Hence, ABCD is a rectangle.

 

 

 

 

Preparation Products

Knockout NEET Sept 2020

An exhaustive E-learning program for the complete preparation of NEET..

₹ 15999/- ₹ 6999/-
Buy Now
Rank Booster NEET 2020

This course will help student to be better prepared and study in the right direction for NEET..

₹ 9999/- ₹ 4999/-
Buy Now
Knockout JEE Main Sept 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
Buy Now
Test Series NEET Sept 2020

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 4999/- ₹ 2999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 11999/-
Buy Now
Exams
Articles
Questions