Constructions| NCERT Solutions| Class 9

NCERT Solutions of Chapter: Constructions. NCERT Solutions along with worksheets and notes for Class 9.

Exercise 11.1

(1) Construct an angle of 900 at the initial point of a given ray and justify the construction.

Ans-

Given – A ray AB with initial point A.

What to construct – Draw an angle of 900 at initial point A.

Steps of Construction –

(a)Draw a ray AB with A as initial point.

(b) Draw an arc of any radius with A as a centre which intersects AB at point D.

(c) Draw an arc with same radius from point D as centre which intersect previous arc at point E.

(d) Again draw an arc of same radius with centre E which intersects previous arc at point F.

(e) Take radius more than half of the arc EF. Draw two arc from point E and F with radius more than half of EF.

(f) Both arcs intersect at point G.

(g) Join A to G. Draw ray AC passing through G.

Therefore, ∠CAB = = 900

 

Diagram of Question 1 of Exercise 11.1 of NCERT Chapter Constructions

(2)Construct an angle of 450 at the initial point of a giben ray and justify the construction.

Ans-

Given – A ray AB with initial point A.

What to construct – Draw an angle of 450 at initial point A.

Steps of Construction –

(a)Draw a ray AB with A as initial point.

(b) Draw an arc of any radius with A as a centre which intersects AB at point D.

(c) Draw an arc with same radius from point D as centre which intersect previous arc at point E.

(d) Again draw an arc of same radius with centre E which intersects previous arc at point F.

(e) Take radius more than half of the arc EF. Draw two arc from point E and F with radius more than half of EF.

(f) Both arcs intersect at point G.

(g) Join A to G. Draw ray AC passing through G.

∠CAB =900

(h) Now, bisect angle CAB.

Take radius more than half of the arc HD. Draw two arcs from point H and D. Arcs intersects at point I.

Join IA. ∠IAB =450.

 

Diagram of Question 2 of Exercise 11.1 of NCERT Chapter Constructions

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Diagram of Question 3(i) of Exercise 11.1 of NCERT Chapter Constructions

(ii)

 

Diagram of Question 3(ii) of Exercise 11.1 of NCERT Chapter Constructions

Diagram of Question 3(iii) of Exercise 11.1 of NCERT Chapter Constructions

Ans-

or ∠IAB = 75°

Diagram of Question 4(i) of Exercise 11.1 of NCERT Chapter Constructions

Diagram of Question 4(ii) of Exercise 11.1 of NCERT Chapter Constructions

Constructions, exercise 11.1, A 4(ii), NCERT, class 9Diagram of Question 4(iii) of Exercise 11.1 of NCERT Chapter Constructions

(5) Construct an equilateral triangle, given its side and justify the construction.

Ans-

Given – One side AB of equilateral triangle ABC.

What to construct – Draw an equilateral triangle ABC.

Steps of construction –

(a)Draw a line AB.

(b)Draw an arc at point A which intersects AB at point D.

(c)Draw another arc from point D with same radius which intersect previous arc at point E.

(d) Join AE. Angle EAB is of measure 600..

(e)Draw an angle of 600 at point B with same procedure.

(f)Let meet both lines at point C.

ABC is required equilateral triangle.

 

 

Diagram of Question 5 of Exercise 11.1 of NCERT Chapter Constructions

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Diagram of Question 1 of Exercise 11.2 of NCERT Chapter Constructions

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Diagram of Question 2 of Exercise 11.2 of NCERT Chapter Constructions

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Diagram of Question 3 of Exercise 11.2 of NCERT Chapter Constructions

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Diagram of Question 4 of Exercise 11.2 of NCERT Chapter Constructions

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Diagram of Question 5 of Exercise 11.2 of NCERT Chapter Constructions

Helping Topics

Constructions

Worksheet Class 9

Practical Geometry

 

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