Math, asked by salariaashutosh04, 1 day ago

prove that a cyclic parallelogram is a rectangle

Answers

Answered by EmperorSoul

182

Given :-

Let ABCD Be A Cyclic Parallelogram

To Prove :-

ABCD Is A Rectangle

Proof:-

➡ A Rectangle Is A Parallelogram With One Angle 90°

So:-

We Have To Prove Angle 90°

Solution :-

Since ABCD Is A Parallelogram

$\small\red{ \boxed{\sf{ \angle \: A= \angle \: C}}}$

$\small\dashrightarrow \sf\boxed{\bold{\pink{Opposite \: Angle \: Of \: ^{Parallelogram \: Are \: Equal}}}}\\$

In Cyclic Parallelogram ABCD :-

$\implies \sf \angle A + \angle \: C = 180 \degree$

$\implies \sf \angle A + \angle \:A = 180 \degree$

$\implies \sf 2\angle A = 180 \degree$

$\implies \sf \angle A = \frac{180 \degree}{2} = 90 \degree$

$\small\dashrightarrow \sf\boxed{\bold{\pink{Sum \: Of \: Opposite \: Angles \: Of ^{\: A \: Cyclic \: Quadrilateral \: Is \: 180°}}}}\\$

So, ABCD Is A Parallelogram With One Angle Is 90°

$\sf\therefore ABCD \ Is \ A \ Rectangle$

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

Answered by 090120015

Previous Question

Next Question

Similar questions

English, 20 hours ago

chocolate is a dessert loved by women . change into active...

English, 20 hours ago

In the last activity, you were pretending to be a character in the story, so you invented a story of your own. Your paragraph was about your experience of painting. it was not about "strong desire_wise action" by Mark Twain.

Computer Science, 20 hours ago

Companies and people often buy and sells stocks. Often they buy the same stock for different prices at different times. Say a person owns 1000 shares a certain stock (such as Checkpoint), she may have bought the stock in amounts of 100 shares over 10 different times with 10 different prices. In this assignment, you will be using a stack for LIFO accounting. You should use an array based...

English, 1 day ago

Fill in the blank with a suitable modal auxiliary. If I were you, I ---------- accept this post. a) will b) would c) would have...

Science, 1 day ago

4.The control centre of a cell is________. (a) cytoplasm (c) vacuoles (b) nucleus (d) mitochondrion.

English, 8 months ago

He has been going_______ the script.

Geography, 8 months ago

5. what are socio economic factors for uneven distribution a population?

Math, 8 months ago

0.25(4y - 3) = 0.5y - 9...

prove that a cyclic parallelogram is a rectangle​