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 and | |
STEP III : Draw bisectors of angles and and mark their intersection point as A. | |
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 and | |
STEP III Draw the bisectors of angles and mark their point of intersection as R. | |
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. |
One 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.
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.
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.
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.
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.
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.
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.
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.
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