Points to Remember: Geometric Constructions Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Points to Remember: Geometric Constructions Notes | EduRev

 Page 1


Geometric 
Construction 
Page 2


Geometric 
Construction 
Geometric construction is drawing a shape (line, angle, triangle, circle etc.) using tools like compass, protractor, straightedge (ruler), etc. This chart will 
help you to construct a similar triangle, division of a line segment and the tangents to a circle from a point outside it. Before going through this chart, 
please be thorough with basic geometric constructions. 
1) Division of a line segment in the ratio m : n
Dividing a line segment AB to the ratio 4 : 3
GEOMETRIC CONSTRUCTION 28
Geometric Construction
1) Draw a line segment AB of 
any length. If the length of a 
line segment AB is given then
draw segment AB of the given 
length.
A B
2) Draw any ray AX, making 
an acute angle with AB.
A
X
B
4) Join Point A
7
 to B.
A 1
A 2
A 3 
A 4
A 5
A 6
A 7
A
X
B
5) Through the point A
4
 (m=4), 
draw a line parallel to A
7
B which 
will intersect AB at a point, name 
that point as C.  So, AC: CB = 4:3
A 1
A 2
A 3 
A 4
A 5
A 6
A 7
A
X
B
C
3) Locate 7 (Sum of 4 and 3) 
points A
1
, A
2
, A
3
 … A
7
 on the 
ray AX such that 
A A
1
= A
1
 A
2
=.…= A
5
 A
6
= A
6
 A
7
 
(means we get 7 equal line 
segments on ray AX).
A 1
A 2
A 3 
A 4
A 5
A 6
A 7
A
X
B
Steps of Constructions 
2) Construction of a similar triangle
     Construct a similar triangle to a given triangle ABC with its sides equal to     of the corresponding sides of the triangle ABC.
3
4
1) First draw the triangle ABC.
A
B
C
2) Draw any ray BX making an
acute angle with BC on the side
opposite to the vertex.
A
B
C
X
3) Locate 4 (the greater of 3 and 
4 in    ) points B
1 
, B
2 
, B
3
 and B
4
 
such that BB
1 
= B
1
B
2
= B
2
B
3
=B
3
B
4
3
4
B 1 B 2 B 3 B 4
A
B
C
X
4) Join B
4
C and draw a line 
through B
3
 parallel to B
4
C to
intersect BC at C’ .
B 1 B 2 B 3 B 4
A
B
C
C’
X
5) Draw a line through C’ 
parallel to the line CA to 
intersect BA at A’ ? A' BC' is the 
required triangle.
B 1 B 2 B 3 B 4
A
A’
B
C
C’
X
Page 3


Geometric 
Construction 
Geometric construction is drawing a shape (line, angle, triangle, circle etc.) using tools like compass, protractor, straightedge (ruler), etc. This chart will 
help you to construct a similar triangle, division of a line segment and the tangents to a circle from a point outside it. Before going through this chart, 
please be thorough with basic geometric constructions. 
1) Division of a line segment in the ratio m : n
Dividing a line segment AB to the ratio 4 : 3
GEOMETRIC CONSTRUCTION 28
Geometric Construction
1) Draw a line segment AB of 
any length. If the length of a 
line segment AB is given then
draw segment AB of the given 
length.
A B
2) Draw any ray AX, making 
an acute angle with AB.
A
X
B
4) Join Point A
7
 to B.
A 1
A 2
A 3 
A 4
A 5
A 6
A 7
A
X
B
5) Through the point A
4
 (m=4), 
draw a line parallel to A
7
B which 
will intersect AB at a point, name 
that point as C.  So, AC: CB = 4:3
A 1
A 2
A 3 
A 4
A 5
A 6
A 7
A
X
B
C
3) Locate 7 (Sum of 4 and 3) 
points A
1
, A
2
, A
3
 … A
7
 on the 
ray AX such that 
A A
1
= A
1
 A
2
=.…= A
5
 A
6
= A
6
 A
7
 
(means we get 7 equal line 
segments on ray AX).
A 1
A 2
A 3 
A 4
A 5
A 6
A 7
A
X
B
Steps of Constructions 
2) Construction of a similar triangle
     Construct a similar triangle to a given triangle ABC with its sides equal to     of the corresponding sides of the triangle ABC.
3
4
1) First draw the triangle ABC.
A
B
C
2) Draw any ray BX making an
acute angle with BC on the side
opposite to the vertex.
A
B
C
X
3) Locate 4 (the greater of 3 and 
4 in    ) points B
1 
, B
2 
, B
3
 and B
4
 
such that BB
1 
= B
1
B
2
= B
2
B
3
=B
3
B
4
3
4
B 1 B 2 B 3 B 4
A
B
C
X
4) Join B
4
C and draw a line 
through B
3
 parallel to B
4
C to
intersect BC at C’ .
B 1 B 2 B 3 B 4
A
B
C
C’
X
5) Draw a line through C’ 
parallel to the line CA to 
intersect BA at A’ ? A' BC' is the 
required triangle.
B 1 B 2 B 3 B 4
A
A’
B
C
C’
X
3) Construction of Tangent to a Circle from a point outside it.
Draw the tangents to a circle with center O from an external point P .
1) Draw any circle with centre ‘O’ and take a 
    point ‘P’ outside the circle. 
2) Join an external point P to the center O. 
    Draw perpendicular bisector of PO. Let 
    M be the midpoint of PO. 
3) Take M as center and MO as radius, draw a 
    circle. Let it intersect the circle at points 
    Q and R. Join PQ and PR. So PQ and PR are the 
    required two tangents.
 
Q 
O 
R 
P 
M 
 
Steps of Constructions 
?
?
?
?
Tangents of the circle are perpendicular to the radius.
Sum of measures of all angles of a triangle and a quadrilateral are 180
o
 and 360
o
 respectively. 
The lengths of the tangents drawn from an external point to a circle are equal. 
The ratios of corresponding sides of similar triangle are same.
O
P
O
M
P
.
.
Activity video - Tangent to a circle on a point on it
How to draw similar triangles Construction of a tangent to a circle from an external point 
Scan the QR Codes to watch our free videos
PLEASE KEEP IN MIND
GEOMETRIC CONSTRUCTION 29
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