The Diagonals of a Parallelogram Bisect Each Other
The Diagonals of a Parallelogram Bisect Each Other
Theorem 4: The diagonals of a parallelogram bisect each other. GIVEN A parallelogram ABCD such that its disgonal AC and BD intersect at O. To Prove OA = OC and OB = OD Proof Since ABCD is a parallelogram. Therefore, AB Now, AB
Again, AB
Now, in <BAO = DCO [From (i)] AB = CD [ and, <ABO = <CDO [From (ii)] So, by ASA congruence criterion
Hence, OA = OC and OB = OD |  |
| Converse Theorem: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram | |
| Given: A quadrilateral ABCD in which the diagonals AC and BD intersect at O such that they bisect each other that is OA = OC and OB = OD | |
To Prove: The Quadrilateral ABCD is a Parallelogram Proof: In OA = OC [Given ]
OB = OD [Given] Therfore But they are alternate interior angles when AB and CD are straight lines and AC is the transversal As they are equal AB || CD Similarly we can prove that AD || BC As both the opposite pair of sides are parallel to each other. Hence ABCD is a parallelogram | |
Illustration: In a parallelogram ABCD the diagonals AC and BD intersect at O, AC = 12.6 cm and BD = 5.8 cm. Find the length of OA, OB, OC and OD.
Solution: ABCD is a parallelogram and diagonals of the parallelogram bisect each other. O is the midpoint of AC OC = OA = 6.3 cm Similarly O is the mid point of BD OD = OB = 2.9 cm Hence OA = 6.3 cm, OB = 2.9cm, OC = 6.3 cm and OD = 2.9cm | |
Students / Parents Reviews [20]
Third 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 ...
Ayan Ghosh
8thAbhyas 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 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
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
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
7thBeing 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
8thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thMy 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
8thI 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
10thMy 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 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.
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10thAbhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of performance in Abhyas exams. He is satisfied with institute.
Yogansh Nyasi
7thAbout 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.
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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
10thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
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10thWhen I have not joined Abhyas Academy, my skills of solving maths problems were not clear. But, after joining it, my skills have been developed and my concepts of science and SST are very well. I also came to know about other subjects such as vedic maths and reasoning.
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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.
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8thMy experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should join Abhyas Academy in tenth class as I am seeing much improvement in Maths and English
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9thUsually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...
