# Welcome to Planet Infinity KHMS

## 26 November, 2007

### Activity Properties of a Cyclic quadrilateral

AIM:
By paper folding, cutting and pasting verify that
1) "The sum of interior opposite angles of cyclic quadrilateral is 180 degrees".
2) "In a cyclic quadrilateral the exterior angle is equal to interior opposite angle".

Material Required:
coloured paper, pair if scissors, sketch pen, carbon paper, geometry box

Procedure:
Step 1: Draw a circle of any radius on a coloured paper and cut it.
Step 2: Paste the circle cut out on a rectangular sheet of paper.
Step 3: By paper folding get chords AB, BC, CD and DA in order.
Step 4: Draw AB, BC, CD & DA. A cyclic quadrilateral ABCD is obtained.
Step 5: Make a replica of cyclic quadrilateral ABCD using carbon paper.
Step 6:Cut the replica into 4 parts such that each part contains one angle .
Step 7:Draw a straight line on a paper.
Step 8:Place angle BAD and angle BCD adjacent to each other on the straight line.Write the observation.
Step 9: Place angle ABC and angle ADC adjacent to each other on the straight line . Write the observation.
Step 10: Produce AB to form a ray AE such that exterior angle CBE is formed.
Step 11: Make a replica of angle ADC and place it on angle CBE . Write the observation.

Observations :

1) angle BAD and angle BCD , when placed adjacent to each other on a straight line, completely cover the straight angle. This means their sum is 180 degrees.

2) angle ABC and angle ADC , when placed adjacent to each other on a straight line, completely cover the straight angle. This means their sum is 180 degrees.

3) The replica of angle ADC completely covers angle CBE.

RESULT: a)The sum of either pair of opposite angle of a cyclic quadrilateral is 180 degrees.

b)In a cyclic quadrilateral, the exterior angle is equal to interior opposite angle.

Anonymous said...

hello,i sakshi of 9thg want to share my experience through this activity which i learn in 'planet infinity'my maths lab of our school.I think its a great experience f0r me and i want to share with you..
The aim of my activity is -'By paper folding and cuting verify that the sum of interior opposite angles of cyclic quadrilateral is 180'and we need coloured paper, geometry box,pair of scissors,sketch pen and carbon paper.first of all take a coloured paper and draw a circle of any radius,cuut it and paste it on a rectangular paper and also make 4 chords in the circle by paper folding but their vertices must be touched to the circumference of circle.Now name those chords say AB,BC,CD,DA and make a replica of cyclic quad.ABCD after that cut that replica into 4 parts so that each part have 1 angle.Then draw a straight line on other paper and place angle BAD anda angle BCD adjacent to each other on that straight line.And then we can observe that when we placed angle BAd and angle BCD on the straight line they completely covers the straight angle and this shows that the sum of opp.angles in cyclic quad.is 180.
I think u all like this n want to try this.I think it's great method to learn maths.........

sakshi gupta
ix-g
31

Anonymous said...

I AM SAKSHI GUPTA OF CLASS IXG ,31 .I AM HERE TO SHARE MY EXPERIENCE IN MATHS LAB OF THIS ACTIVITY .IT IS ACTIVITYBY WHICH WE ABLE TO VISUALISE THE CONCEPT OF SUM OF INTERIOR OPPOSITE ANGLES OF CYCLIC QUADRILATERAL BY HANDS ON PAPER FOLDING .ILIKE THIS ACTIVITY IN MA6THS LAB .WE DO LOTS OF SUCH ACTIVIES WITH FUN. I LOVE THIS WAY OF LARING MATHS.

Ridz!*!>>.. said...

hello!..friends! Ridam here! i'm in IX-g.
Till the starting of this session, i didn't had any interests in studying maths. For me, studying maths was like killing myself. I hated maths a lot because i usually got confused while doing it. I mixed everything up.
When i joined PLANET INFINITY- my maths lab, i felt that maths is not that hard for me. This Planet Infinity made maths so easy for me. I still don't believe that now i can understand each n every concept of maths so easily n i feel as if i m playing a game with numbers while studying maths. This PLANET INFINITY changed my thinking about maths.
Now, i want to tell u which part was the most interesting for me. Personally, i found the whole combo of lab awesome n easy but i would like to tell u which was the most interesting one for me.
my aim for this activity is..
by paper folding n cuting, verify that the sum of interior opposite angels of cyclic quadrilateral is 180'; for doing this, i need some cloured paper, pair of scissors, sketchpen, carbon paper n my geometry box, ofcourse.
Now, first of all take a coloured paper n draw a circle of any radius and by paper folding, make 4 chords on it. then give them name, say, AB,BC,CD,DA. Then, paste it on the sheet.We'll obsereve a cyclic quadrilateral is formed. Now, make a replica of this cyclic quadrilateral ABCD using carbon paper.After making the replica, cut it into 4 parts but while cutting the parts, it should be kept in mind that every cut should contain 1 angle. Then, draw straight line on the paper and place angle BAD and angle BCD adjacent to each other on that straight line.
After doing this, we'll observe that when these angles are placed adjacent to each other on a straight line, they completely overcome the straight line. This means that their sum is 180'.
I hope that you must have understood what I've explained.
It was really fun doing it...!!

RiDaM AgGarWaL
IX-'G'
17 {RoLl NuMbeR}

Anonymous said...

thanx it helped me for my hands on activity