Diagonals of Square Are Equal and Perpendicular to Each Other.
Diagonals of Square Are Equal and Perpendicular to Each Other.
Theorem: In a square the diagonals are equal and perpendicular to each other.
Given: A square ABCD. To Prove: AC = BD and AC and BC intersect perpendicularly. Proof: In AD = BC [ AB = AB [ Common] Therfore As ABCD is a square Therefore it is a parallelogram. Also diagonals of a parallelogram bisect each other.
In BO = DO [ From Equation (1)] BC = CD [ Sides of a square] OC = OC [ Common ] Therfore
But
Similarly we can prove that Hence Proved that In a square the diagonals are equal and perpendicular to each other. |  |
| Theorem : If the diagonals of a parallelogram are equal and intersect at right angles, then the parallelogram is a square. | |
Given : ABCD is a parallelogram, such that AC = BD and AC To Prove: ABCD is a square Proof: In AO = OC [ Diagonals of parallelogram bisect each other] BO = OB [ Common] Therefore AB = BC [CPCT] As ABCD is a IIgm and the adjacent sides are equal AB = BC Therefore AB = BC = CD= DA. In AD = BC [ Proved above] BD = AC [Given] AB = AB [ Common] Therfore
As ABCD is a parallelogram, AD || BC Now AD || BC and AB is the transversal
Now ABCD is a IIgm in which all sides are equal and one angle is | |
Illustration: If the side of a square ABCD whose diagonals intersect at O is 6cm find the length of OA and OB;
Solution: As the diagonals of a square are equal and bisect each other perpendicularly We can say that OA = OB = x(say) ..............(1) and AB = 6cm ...................(2) [Given] Now
Substituting the values from Eq (1) and (2), we get
Hence OA = OB = | |
PQRS is a square. PR and SQ intersects at O. State the measure of | |||
| Right Option : B | |||
| View Explanation | |||
If the side of a square ABCD whose diagonals intersect at O is | |||
| Right Option : A | |||
| View Explanation | |||
ABCD is a square. AC and BD intersect at O. State the measure of | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [20]
It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
Manya
8thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thAbhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary because of Abhyas.Teacher have very friendly atmosphere also.
Manish Kumar
10thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
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Yogansh Nyasi
7thMy experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills developed and now I am the first one to give the answer of teachers question.
Upmanyu Sharma
7thAbhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...
Shreya Shrivastava
8thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
10thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thAbhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thAbhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.
Barkha Arora
10thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
10thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
