__9th (IX) Construction of Triangle CBSE and NCERT Study Guide__

Target to study:

(1) Use only ruler and compass while drawing constructions.

(2) Protractor may be used for drawing non-standard angles.

(3) Constructions of a triangle given its base, a base angle and the difference of the other two sides.

(4) Constructions of a triangle given its perimeter and its two base angles.

Construct a triangle ABC in which BC = 5 cm, < B = 60° and the sum of the other two sides is 7 cm
Step of Constructions: (i) Draw BC = 5 cm. (ii) Draw < XBC = 60° (iii) On the ray BX, mark off point D such that BD = 7 cm. (iv) Join D to C. (v) Draw perpendicular bisector EF of CD. Let it intersects BD at A. (vi) Join A to C. ABC is the required triangle Construct a Triangle ABC in which < B = 45°, <C = 60° and AB + BC + AC = 13 cm.
Step of constructions: (i) Draw XY = 13 cm. (ii) Draw < MXY = 45° and < NYX = 60° (iii) Draw angle bisectors of < MXY and < NYX, meeting at a point, say A. (iv) Draw perpendicular bisector of XA and YA, meeting XY at B and C respectively. (v) Join A to B and A to C. ABC is the required triangle |
Construct a Triangle ABC in which BC = 5.5 cm, < B = 30° and AB – AC = 2 cm.
Step of constructions: (i) Draw BC = 5.5 cm. (ii) Draw < XBC = 30° (iii) On the ray BX, mark off point D such that BD = 2 cm. (iv) Join D to C. (v) Draw perpendicular bisector EF of CD. Let it intersects BX at A. (vi) Join A to C. ABC is the required triangle. |

Board Questions:

1. Draw any acute angle. Name as <XYZ. Bisect it. Measure and name the angles so obtained.

2.Draw a line segment QR = 5 cm. Construct pependiculers at point Q and R respectively. Name them as QX and RY. Are they both parallel ?

3.Draw a line segment PQ = 8.4 cm Divide PQ into four equal parts using ruler and compass.

4.Draw a line segment XY of length 96 mm. Using ruler and compass, measure the length 1/2 XY.

5.Construct a right angle triangle whose base is of length 4 cm and length of perpendicular is 3 cm. Now construct perpendicular bisectors of any two sides. Where these bisectors intersect ?

6.Give reasons :

(a) Construction of an angle of 22.5 degree is possible with the help of ruler and compass.

(b) It is not possible to construct a triangle ABC, given that BC = 7 cm, <B = 45 deg. and AB - AC = 10 cm

(c) We can construct an angle of 67.5 deg using ruler and compass.

(d) Construction of triangle DEF, if EF = 5.5 cm, < E = 75 deg. and DE - DF = 2 cm is possible

7.Using ruler and compass, construct an angle of 90 deg. at the initial point of a given ray.

8.(a) State Angle Sum Property of a triangle.

(b) Is it possible to construct triangle ABC if perimeter of the triangle is 11 cm, base angles <A = 60 deg. and <B = 70 deg.

(c) Is it possible to construct triangle EFG, , if EF + FG + GE = 11 cm , < E = 105 deg. and <F= 90 deg.

(d) Is it possible to construct triangle XYZ if perimeter is 12.5 cm, <X = 75 deg. and <Y = 30 deg.

9.Using ruler and compass, construct an angle of 135 deg. at the initial point of a given ray.

10.Construct an equilateral triangle of side 5.2 cm. each. Now construct bisector of any two angle . where does their intersecting point lies?

11.Construct a triangle ABC in which BC = 4cm and ∠B = 60° and AB+AC = 6cm.

12. Construct a triangle with perimeter 10cm and base angles 60° and 45°. Write the steps of construction.

13.Construct an equilateral triangle whose altitude measures 5.5 cm.

14. Construct a triangle ABC in which BC = 7 cm, <B = 60 deg. and AC - AB = 2.4 cm.

15. Draw an angle of 60 deg. using protector and bisect it and give justification.

16. using rular and compass construct 4 <XYZ if <XYZ = 20 deg.

17. Construct a square whose side mesure 5 cm.

18.Draw an angle of mesure 135 deg. Verify using protector.

19.Construct a triangle XYZ with perimeter 14 one side is of length 5cm and <x= 45°.

20.Construct an equilateral triangle if one of its altitude = 4.5 cm

1. Draw any acute angle. Name as <XYZ. Bisect it. Measure and name the angles so obtained.

2.Draw a line segment QR = 5 cm. Construct pependiculers at point Q and R respectively. Name them as QX and RY. Are they both parallel ?

3.Draw a line segment PQ = 8.4 cm Divide PQ into four equal parts using ruler and compass.

4.Draw a line segment XY of length 96 mm. Using ruler and compass, measure the length 1/2 XY.

5.Construct a right angle triangle whose base is of length 4 cm and length of perpendicular is 3 cm. Now construct perpendicular bisectors of any two sides. Where these bisectors intersect ?

6.Give reasons :

(a) Construction of an angle of 22.5 degree is possible with the help of ruler and compass.

(b) It is not possible to construct a triangle ABC, given that BC = 7 cm, <B = 45 deg. and AB - AC = 10 cm

(c) We can construct an angle of 67.5 deg using ruler and compass.

(d) Construction of triangle DEF, if EF = 5.5 cm, < E = 75 deg. and DE - DF = 2 cm is possible

7.Using ruler and compass, construct an angle of 90 deg. at the initial point of a given ray.

8.(a) State Angle Sum Property of a triangle.

(b) Is it possible to construct triangle ABC if perimeter of the triangle is 11 cm, base angles <A = 60 deg. and <B = 70 deg.

(c) Is it possible to construct triangle EFG, , if EF + FG + GE = 11 cm , < E = 105 deg. and <F= 90 deg.

(d) Is it possible to construct triangle XYZ if perimeter is 12.5 cm, <X = 75 deg. and <Y = 30 deg.

9.Using ruler and compass, construct an angle of 135 deg. at the initial point of a given ray.

10.Construct an equilateral triangle of side 5.2 cm. each. Now construct bisector of any two angle . where does their intersecting point lies?

11.Construct a triangle ABC in which BC = 4cm and ∠B = 60° and AB+AC = 6cm.

12. Construct a triangle with perimeter 10cm and base angles 60° and 45°. Write the steps of construction.

13.Construct an equilateral triangle whose altitude measures 5.5 cm.

14. Construct a triangle ABC in which BC = 7 cm, <B = 60 deg. and AC - AB = 2.4 cm.

15. Draw an angle of 60 deg. using protector and bisect it and give justification.

16. using rular and compass construct 4 <XYZ if <XYZ = 20 deg.

17. Construct a square whose side mesure 5 cm.

18.Draw an angle of mesure 135 deg. Verify using protector.

19.Construct a triangle XYZ with perimeter 14 one side is of length 5cm and <x= 45°.

20.Construct an equilateral triangle if one of its altitude = 4.5 cm

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