Theorem 2: The diagonals of a rectangle are of equal length.
Given : PQRS is a rectangle. To Prove : PR = QS Proof:As each rectangle is a parallelogram and PQRS is a rectangle Therefore PQRS is a parallelogram PS = QR '................(1) [ Opposite sides of a parallelogram] As each angle of a rectangle is a right angle In PS = QR [ From Equation 1 ] [ Each right angle ] RS = RS [ Common ] [By SAS Congruence Criteria] PR = QS [ CPCT] Hence Proved |
Converse of Theorem 2: If the diagonals of a parallelogram are of equal length, it is a rectangle.
Given : PQRS is a parallelogram such that PR = QS. To Prove : PQRS is a rectangle Proof: In PR = QS [ Given ] PS = QR [ Opposite sides of parallelogram ] RS = RS [ Common ] [By SSS Congruence Criteria] --------(1) [ CPCT] As PQRS is a parallelogram, PS || QR Now PS || QR and RS is the transversal [ Co interior angles are supplementary ] [ Replacing R from equation 1] Now PQRS is a parallelogram in which one angle is a right angle. Therefore PQRS is a rectangle Hence Proved |
Illustration: The diagonals of a rectangle PQRS intersect at O, If
Solution: PQRS is a rectangle and we know that diagonals of a rectangle are equal Each rectangle is aparallelogram and we know that diagonals of a parallelogram bisect each other Therefore OS = OR [ Because when diagonals are equal halves are equal ] In , As OS = OR [Angles opposite equal side are equal ] Now is the exterior angle of [ because ] Now each angle of a rectangle is a right angle. |
|
The diagonals of a rectangle PQRS intersect at O, If | |||
Right Option : B | |||
View Explanation |
The diagonals of a rectangle PQRS intersect at O, If Find . | |||
Right Option : A | |||
View Explanation |
ABCD is a rectangle with . Determine . | |||
Right Option : A | |||
View Explanation |
A 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.
It 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
Being 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.
My 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.
Abhyas 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.
About 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.
Abhyas 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.
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.
It 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.
My 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.