Construct a triangle similar to a given triangle as per given scale factor
Construct a triangle similar to a given triangle as per given scale factor
Construct a triangle similar to a given triangle as per given scale factor:
Scale Factor:
The ratio m : n of the side of the triangle to be constructed with the corresponding sides of the given triangle is knwon as their scale factor.
In this construction, there are two diferent situations:
(I) Steps of construction when m<n :
(i) Construct the given triangle ABC by using the given data.
(ii) Take any one of the three side of the given triangle as base. Let AB be the base of the given triangle.
(iii) At one end, say A, of the base AB draw a ray AX making a suitable acute angle with AB below the base AB.
(iv) Along AX mark n points such that
(v) Join
(vi) Draw parallel to
which meets AB at B.
(vii) From B1 draw B1C1 BC meeting AC at C1.
Triangle AB1C1 is the required triangle each of whose sides is of the corresponding side of
Example: Construct a in which AB = 5cm, BC = 6 cm and AC = 7 cm. Now, construct a triangle similar to
such that each of its sides is two-third of the corresponding sides of
.
SOLUTION:
Steps of Construction:
(i) Draw a line segment AB = 5cm.
(ii) With A as centre and radius = 7cm, draw an arc above AB.
(iii) With B as centre and radius = 6 cm, draw another arc, intersecting the arc drawn in step ii) at C.
(iv) Join AC and BC to obtain .
(v) Below AB, draw a ray AX making a suitable acute angle with AB on opposite side of C with respect to AB.
(vi) Draw three arcs (greater of 2 and 3 in 2/3) intersecting the ray AX at such that
(vii) Join
(viii) Draw meeting AB at B1.
(ix) From B1, draw , meeting AC at C1.
AB1C1 is the required triangle, each of the whose sides is two-third of the corresponding sides of
(II) Steps of construction when m>n :
(i) Construct the given triangle by using the given data.
(ii) Take any one of the three sides of the given triangle and consider it as th base. Let AB be the base of the given triangle.
(iii) At one end, say A, of base AB draw a ray AX making a suitable acute angle with base AB on the opposite side of the vertex C with respect to AB.
(iv) Draw arcs (large of m and n) intersecting the ray AX at such that
(v) Join to B.
(vi) Draw a line through parallel to
, intersecting the extended line segement AB at B1.
(vii) Draw a line through B1 parallel to BC intersecting the extended line segment AC at C1
(viii) so obtained is the required triangle.
Example: Draw a triangle ABC with side BC = 7 cm. .Construct a triangle whose sides are (4/3) times the corresponding side of
SOLUTION:
Steps of Construction:
(i) Draw BC = 7 cm.
(ii) Draw a ray BX and CY such that and
Suppose BX and CY intersect each other at A.
so obtained is the given triangle.
(iii) Draw a ray BZ making a suitable acute angle with BC on oppsosite side of vertex A with respect to BC.
(iv) Draw four (greater of 4 and 3 in 4/3) arcs intersecting the ray BZ at such that
(v) Join to C and draw a line through
parallel to
intersecting the extended line segement BC at C1.
(vi) Draw a line through C1 parallel to CA intersecting the extended line segement BA at A1.
Triangle A1BC1 so obtained is the required triangle.
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Abhyas 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...
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Ayan Ghosh
8thAbhyas 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...
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Om Umang
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Eshan Arora
8thThird 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
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Upmanyu Sharma
7thOne 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
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
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9thThe 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
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.
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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...
