Constructions Exercise 17.3

Question: 1

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

Solution:

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:

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:

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 ∠A = 120°, AB = AC = 3 cm. Measure ∠B and ∠C.

Solution:

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 ∠B = ∠C = 30°.
 

Question: 5

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

Solution:

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 ∠B = 45°. Also, draw a perpendicular from A on BC.

Solution:

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 ∠B = 60°. Also, draw the bisector of angles C and A of the triangle, meeting in a point O. Measure ∠COA.

Solution:

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°.