Congruence of Triangles
Congruence of Triangle
Congruence means that one figure will exactly superimpose the other figure. Two congruent line segments have the same length and conversely two lines segments of equal length are congruent. or we can say that two line segments are congruent if and only if their lengths are equal. Similarly two angles are congruent if and only if their measures are equal, or we can say that two angles BAC and EDF are congruent if m
Two triangles are congruent if and only if one of them can be made to superpose on the other, so as to cover it exactly. Let be two congruent triangles. Then, we can superpose
on
, so as to cover it exactly. In such a superposition the vertices of
will fall on the vertices of
, in some order. Let us assume that the vertex A falls on vertex D, vertex B on vertex E and vertex C on vertex F.
Then, side AB falls on DE, BC on EF and CA on FD. Also superposes on the corresponding angle
and
. Thus, the order in which the vertices match, automatically determines a correspondence between the sides and angles of the two triangles. And, if the superposition is exact i.e. the triangles are congruent, the corresponding sides and angles are congruent. Consequently, we get six equalities three of the corresponding sides and three of the corresponding angles. If
superposes on
exactly such that the vertices of
fall on the vertices of
in the following order
|
Then, we have the following six qualities |
 |
Congruence Relation
From the definition of congruence of two triangles, we obtain the following results:
(i) Every triangle is congruent to itself i.e.,
(ii) If , then
(iii) If , and
, then
Note: It is important to write the correspondence of vertices correctly for writing of congruence of triangles in symbolic form because but
and the symbolic form is used to write corresponding parts of congruent triangles {C.P.C.T.}
Which of the following is not a criteria for congruency ? | |||
| Right Option : D | |||
| View Explanation | |||
If two triangles | |||
| Right Option : D | |||
| View Explanation | |||
If | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [20]
Abhyas 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
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
7thThe experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confidence to overcome competitive exams. One of the best institutes for secondary education.
Aman Kumar Shrivastava
10thMy 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
Hridey Preet
9thMy 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
8thWhen 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.
Sharandeep Singh
7thAbhyas 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
10thUsually 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...
Anika Saxena
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
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
8thAbout 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
8thIt 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
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
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
10thOne 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
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
8thMy 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
7thIn 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...
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
10thIt 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.
