Diagonals of a Parallelogram: We know that parallelogram is a quadrilateral in which both the opposite pair of sides are parallel and equal to each other. The diagonal of a parallelogram divides it into two congruent triangles.
Theorem 1: A diagonal of a parallelogram divides it into two congruent triangles.
Given A parallelogram ABCD.
To prove A diagonal, say, AC, of parallelogram ABCD divides it into congruent triangles ABC and CDA i.e. ABC CDA
Construction Join AC. Proof Since ABCD is a parallelogram. Therefore, AB DC and AD BC Now, AD BC and transversal AC intersects them at A and C respectively. <DAC = <BCA ....(i) [ Alternate interior angles ] Again, AB DC and transversal AC intersects them at A and C respectively. Therefore, <BAC = <DCA ....(ii) [ Alternate interior angles ] Now, in s ABC and CDA, we have <BCA = <DAC [From (i)] AC = AC [ Common side ] <BAC = <DCA [ From (i)] So, by ASA congruence criterion, we have ABC CDA | |
ILLUSTRATION: Find the value of x and y in the figure | |
Solution: In the figure ABCD is a parallelogram and AC is the diagonal. We know that the diagonal of a parallelogram divides it into two congruent triangles
[ Corresponding parts of congruent triangle]
Similarly [ Corresponding parts of congruent triangle]
|
In the following figure, ABCD is a parallelogram. The diagonal AC divides this parallelogram into which congruent triangles? | |||
Right Option : B | |||
View Explanation |
In the following figure, The diagonal of parallelogram divides parallelogram into which congruent triangles? | |||
Right Option : B | |||
View Explanation |
In the figure, the diagonal divides parallelogram into which two congruent triangles? | |||
Right Option : C | |||
View Explanation |
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.
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 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.
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.
I 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
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.
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.
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.
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.
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.