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# 04 - Let's Recap - Constructions - Class 10 - Maths Class 10 Notes | EduRev

## Class 10 : 04 - Let's Recap - Constructions - Class 10 - Maths Class 10 Notes | EduRev

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CONSTRUCTIONS

Construction is very important in geometry which helps to develop the skill of
drawing figures accurately.

Division of a line segment:

In order to divide a line segment internally in a given ratio m: n, where both m and
n are positive integers, the following steps are followed:

Given: A line segment PQ and ratio m: n.
Required: To divide line segment PQ in the ratio m: n.
Steps of construction:
 Draw a line segment PQ of given length by using a ruler. Draw any ray PX
making a suitable acute angle with PQ.
 Along PX draw (m + n) arcs intersecting the rays PX at P
1
, P
2
,.....P
m
....P
m+n.

 Join the points i.e. Q P
m+n
.
 Draw a line through point  P
m
parallel to P
m+n
.
 We get one point A; this point divides PQ internally in the ratio m: n.

Page 2

CONSTRUCTIONS

Construction is very important in geometry which helps to develop the skill of
drawing figures accurately.

Division of a line segment:

In order to divide a line segment internally in a given ratio m: n, where both m and
n are positive integers, the following steps are followed:

Given: A line segment PQ and ratio m: n.
Required: To divide line segment PQ in the ratio m: n.
Steps of construction:
 Draw a line segment PQ of given length by using a ruler. Draw any ray PX
making a suitable acute angle with PQ.
 Along PX draw (m + n) arcs intersecting the rays PX at P
1
, P
2
,.....P
m
....P
m+n.

 Join the points i.e. Q P
m+n
.
 Draw a line through point  P
m
parallel to P
m+n
.
 We get one point A; this point divides PQ internally in the ratio m: n.

Construction of a triangle similar to a given triangle:
Suppose we are given ABC ? and we have to construct a triangle whose sides are
equal to
n
m
of the corresponding sides of ABC ? .
 If m > n, then the triangle to be constructed is larger than the given triangle.
 If m < n, then the triangle to be constructed is smaller than the given
triangle.
Scale Factor: Scale factor means the ratio of the sides of the triangle to be
constructed with corresponding sides of the given triangle.

Construction of tangents to a circle:

1) To draw tangents to a circle from a point outside it, when centre of the
Circle is known:
Given: A circle is given with centre as O and radius r, and an external point A
Required: To draw the tangents to the circle from the point A.
Steps of construction:
 Join OA, and bisect it.
 Let R be the midpoint of OA.
 Taking point R as centre and RO as radius draw a circle to intersect the
given circle at two points X and Y.
 Draw a rays AX and AY.
 Ray AX and AY are the required tangents from A to given circle.

Page 3

CONSTRUCTIONS

Construction is very important in geometry which helps to develop the skill of
drawing figures accurately.

Division of a line segment:

In order to divide a line segment internally in a given ratio m: n, where both m and
n are positive integers, the following steps are followed:

Given: A line segment PQ and ratio m: n.
Required: To divide line segment PQ in the ratio m: n.
Steps of construction:
 Draw a line segment PQ of given length by using a ruler. Draw any ray PX
making a suitable acute angle with PQ.
 Along PX draw (m + n) arcs intersecting the rays PX at P
1
, P
2
,.....P
m
....P
m+n.

 Join the points i.e. Q P
m+n
.
 Draw a line through point  P
m
parallel to P
m+n
.
 We get one point A; this point divides PQ internally in the ratio m: n.

Construction of a triangle similar to a given triangle:
Suppose we are given ABC ? and we have to construct a triangle whose sides are
equal to
n
m
of the corresponding sides of ABC ? .
 If m > n, then the triangle to be constructed is larger than the given triangle.
 If m < n, then the triangle to be constructed is smaller than the given
triangle.
Scale Factor: Scale factor means the ratio of the sides of the triangle to be
constructed with corresponding sides of the given triangle.

Construction of tangents to a circle:

1) To draw tangents to a circle from a point outside it, when centre of the
Circle is known:
Given: A circle is given with centre as O and radius r, and an external point A
Required: To draw the tangents to the circle from the point A.
Steps of construction:
 Join OA, and bisect it.
 Let R be the midpoint of OA.
 Taking point R as centre and RO as radius draw a circle to intersect the
given circle at two points X and Y.
 Draw a rays AX and AY.
 Ray AX and AY are the required tangents from A to given circle.

2) To draw tangents to a circle from a point outside it, when centre of the
circle is not known:

Given: A circle and a point V outside it
Required: To draw tangents from point V to the circle.
Steps of construction:
 Draw a secant VXY to intersect the circle at two points X and Y.
 Extend VX to point Z, such that VX= VZ,
 With ZY as diameter draw semi-circle.
 Draw VW perpendicular to ZY, intersecting semicircle drawn at W.
 Taking VW as radius and V as centre draw an arcs intersecting given circle
at R and R’
 Draw rays VR and VR’
 Rays VR and VR’ are the required tangents.

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## Mathematics (Maths) Class 10

51 videos|346 docs|103 tests

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