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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