NCERT Revision Notes for Chapter 11 Constructions Class 10 Maths
CBSE NCERT Revision Notes1
Q. Draw Line segment PQ=9cm and divide it in the ratio 2:5. Justify your construction.
Answer
Draw Line Segment PQ=9cm
Draw a Ray PX, making an acute angle with PQ.
Mark 7 points A1 , A2 , A3 … A7 along PX such that
PA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6 A7
Join QA7
Through the point A2 , draw a line parallel to A7Q by making an angle equal to
∠PA 7Q at A2 , intersecting PQ at point R.
PR:RQ = 2:5
Justification:
We have A2R || A7Q
2
Construction of a triangle similar to a given triangle as per the given scale factor when Scale Factor is less than 1
Draw a ΔABC with sides BC = 8 cm, AC = 7 cm, and ÐB = 70°. Then, construct a similar triangle whose sides are (3/5)th of the corresponding sides of the 
ABC.
Answer
Steps of construction:
Draw BC = 8 cm
At B, draw ∠XBC = 70°
With C as centre and radius 7 cm, draw an arc intersecting BX at A.
Join AB, and DABC is thus obtained.
Draw a ray , making an acute angle with BC.
Mark 5 points, B1 , B2 , B3, B4 , B5 , along BY such that
BB1 = B1B2 = B2B3 = B3B4 = B4B5
Join CB5
Through the point B3 , draw a line parallel to B5C by making an angle equal to
∠BB5 C, intersecting BC at C´.
Through the point C´, draw a line parallel to AC, intersecting BA at A´. Thus, ΔA´BC´ is Required Triangle.
Justification
Using BPT.
3
Construction of a triangle similar to a given triangle as per the given scale factor when Scale Factor is more than 1
Q. Construct an isosceles triangle with base 5 cm and equal sides of 6 cm. Then, construct another triangle whose sides are of the corresponding sides of the (4/3)th of first triangle .
Answer
Steps of construction:
Draw BC = 5 cm
With B and C as the centre and radius 6 cm, draw arcs on the same side of BC, intersecting at A.
Join AB and AC to get the required ΔABC.
Draw a ray , making an acute angle with BC on the side opposite to the vertex A.
Mark 4 points B1 , B2 , B3, B4 , along BX such that
BB1 = B1 B2 = B2B3 = B3B4
Join B3C. Draw a line through B4 parallel to B3C, making an angle equal to ∠BB3C
intersecting the extended line segment BC at C´.
Through point C´, draw a line parallel to CA, intersecting extended BA at A´.
The resulting ΔA´BC´ is the required triangle.
4
Construction of tangents to a circle
Q. Draw a circle of radius 3 cm. From a point 5 cm away from its centre, construct a pair
Answer
Steps of construction:
1. Draw a circle with centre O and radius 3 cm. Take a point P such that OP = 5
cm, and then join OP.
2. Draw the perpendicular bisector of OP. Let M be the mid point of OP.
3. With M as the centre and OM as the radius, draw a circle. Let it intersect the
previously drawn circle at A and B.
4. Joint PA and PB. Therefore, PA and PB are the required tangents. It can be observed that PA=PB=4cm.
