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Constructions Exercise 17.3

Question: 1

Draw △ABC in which AB = 3 cm, BC = 5 cm and ∠= 70°.

Solution:

Constructions Exercise 17.3 Question: 1

Steps of construction:

  • Draw a line segment AB of length 3 cm.

  • Draw ∠XBA=70°.

  • Cut an arc on BX at a distance of 5 cm at C.

  • Join AC to get the required triangle.
     

Question: 2

Draw △ABC  in which ∠A=70°., AB = 4 cm and AC= 6 cm. Measure BC.

Solution:

Constructions Exercise 17.3 Question: 2

Steps of construction:

  • Draw a line segment AC of length 6 cm.

  • Draw ∠XAC=70°.

  • Cut an arc on AX at a distance of 4 cm at B.

  • Join BC to get the desired triangle.

  • We see that BC = 6 cm.
     

Question: 3

Draw an isosceles triangle in which each of the equal sides is of length 3 cm and the angle between them is 45°.

Solution:

Constructions Exercise 17.3 Question: 3

Steps of construction:

Draw a line segment PQ of length 3 cm.

Draw ∠QPX=45°.

Cut an arc on PX at a distance of 3 cm at R.

Join QR to get the required triangle.
 

Question: 4

Draw △ABC  in which ∠= 120°, AB = AC = 3 cm. Measure ∠B and ∠C.

Solution:

Constructions Exercise 17.3 Question: 4

Steps of construction:

  • Draw a line segment AC of length 3 cm.

  • Draw ∠XAC = 120°.

  • Cut an arc on AX at a distance of 3 cm at B.

  • Join BC to get the required triangle.

By measuring, we get ∠= ∠= 30°.
 

Question: 5

Draw △ABC  in which ∠= 90° and AC = BC = 4 cm.

Solution:

Constructions Exercise 17.3 Question: 5

Steps of construction:

  • Draw a line segment BC of length 4 cm.

  • At C, draw ∠BCY=90°.

  • Cut an arc on CY at a distance of 4 cm at A.

  • Join AB. ABC is the required triangle.
     

Question: 6

Draw a triangle ABC in which BC = 4 cm, AB = 3 cm and ∠= 45°. Also, draw a perpendicular from A on BC.

Solution:

Constructions Exercise 17.3 Question: 6

Steps of construction:

  • Draw a line segment AB of length 3 cm.

  • Draw an angle of 45° and cut an arc at this angle at a radius of 4 cm at C.

  • Join AC to get the required triangle.

  • With A as centre, draw intersecting arcs at M and N.

  • With centre M and radius more than half of MN, cut an arc on the opposite side of A.

  • With N as centre and radius the same as in the previous step, cut an arc intersecting the previous arc at E.

  • Join AE, it meets BC at D, then AE is the required perpendicular.
     

Question: 7

Draw a triangle ABC with AB = 3 cm, BC = 4 cm and ∠= 60°. Also, draw the bisector of angles C and A of the triangle, meeting in a point O. Measure ∠COA.

Solution:

Constructions Exercise 17.3 Question: 7

Steps of construction:

Draw a line segment BC = 4 cm.

Draw ∠CBX = 60°.

Draw an arc on BX at a radius of 3 cm cutting BX at A.

Join AC to get the required triangle.

Angle bisector for angle A:

  • With A as centre, cut arcs of the same radius cutting AB and AC at P and Q, respectively.

  • From P and Q cut arcs of same radius intersecting at R.

  • Join AR to get the angle bisector of angle A.

Angle bisector for angle C:

  • With A as centre, cut arcs of the same radius cutting CB and CA at M and N, respectively.

  • From M and N, cut arcs of the same radius intersecting at T

  • Join CT to get the angle bisector of angle C.

Mark the point of intersection of CT and AR as 0.

Angle ∠COA = 120°.


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