Construction of a triangle given its perimeter and its two base angles
Construction of a triangle given its perimeter and its two base angles
Construction of Triangle Given Its Perimeter and Its Two Base Angles: In order to construct a triangle of given perimeter and two base angles, we follow the following steps:
Steps of Construction: Obtain the perimeter and the base angles of the triangle.Let ABC be a triangle of perimeter p cm and base BC.
STEP I Draw a line segment XY equal to the perimeter p of STEP II Construct |  |
| STEP III : Draw bisectors of angles |  |
| STEP IV: Draw the perpendicular bisectors PQ, RS of XA and YA meeting XY in B and C respectively. |  |
| STEP V Join AB and AC to obtain the required triangle ABC. |  |
Justification: For the justification of the construction, we observe that B lies on the perpendicular bisector of AX.
XB = AB
[ Angles opposite to equal sides are equal]
Similarly, C lies on the perpendicular bisector of AY.
YC = AC
Now, XY = XB + BC + CY
XY = AB + BC + AC
In we
[Exterior angle is equal to the sum of interior opposite angle]
[because the angles are equal Proved above]
[ AX is the bisector ]
= [By Step II of Construction]
In we have
[Exterior angle is equal to the sum of interior opposite angle]
[because the angles are equal Proved above]
[ AY is the bisector ]
[By Step II of Construction]
Example: Construct a triangle PQR whose perimeter is equal to 14 cm, and
.
SOLUTION To draw we follow the following steps:
Steps of Construction:
STEP I Draw a line segment XY = 14 cm STEP II Construct |  |
| STEP III Draw the bisectors of angles |  |
| STEP IV Draw right bisector AB, CD of RX and RY meeting XY at P and Q respectively. |  |
| STEP V Join PR and QR to obtain the required triangle PQR. |  |
Students / Parents Reviews [20]
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.
Archit Segal
7thAbhyas 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
10thI 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
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...
Aman Kumar Shrivastava
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.
Sharandeep Singh
7thAbhyas 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 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
8thIt 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
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
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
Hridey Preet
9thThird 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
8thUsually 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
8thWe 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
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
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 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
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
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
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
10thMy 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.
