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Constructions Exercise 17.4

Question: 1

Construct △ABC in which BC= 4 cm, ∠B=50° and ∠C=70°.

Solution:

Constructions Exercise 17.4 Question: 1

Steps of construction:

  • Draw a line segment BC of length 4 cm.

  • Draw ∠CBX such that ∠CBX=50°.

  • Draw ∠BCY with Y on the same side of BC as X such that ∠BCY=70°.

  • Let CY and BX intersect at A.

  • ABC is the required triangle.

Question: 2

Draw △ABC in which BC= 8 cm, ∠B=50° and ∠A=50°.

∠ABC+∠BCA+∠CAB=180°

∠BCA=180°−∠CAB−∠ABC

∠BCA=180°−100°=80°

Solution:

Constructions Exercise 17.4 Question: 2

Steps of construction:

  • Draw a line segment BC of length 8 cm.

  • Draw ∠CBX such that ∠CBX=50°.

  • Draw ∠BCY with Y on the same side of BC as X such that ∠BCY=80°.

  • Let CY and BX intersect at A.

Question: 3

Draw △ABC in which ∠Q=80°, ∠R=55° and QR = 4.5 cm. Draw the perpendicular bisector of side QR.

Solution:

Constructions Exercise 17.4 Question: 3

Steps of construction:

  • Draw a line segment QR = 4.5 cm.

  • Draw ∠RQX=80° and ∠QRY=55°.

  • Let QX and RY intersect at P so that PQR is the required triangle.

  • With Q as centre and radius more that 2.25 cm, draw arcs on either sides of QR.

  • With R as centre and radius more than 2.25 cm, draw arcs intersecting the previous arcs at M and N.

  • Join MN

MN is the required perpendicular bisector of QR.

Question: 4

Construct △ABC in which AB = 6.4 cm, ∠A=45° and ∠B=60°

Solution:

Constructions Exercise 17.4 Question: 4

Steps of construction:

Draw a line segment AB = 6.4 cm.

Draw ∠BAX=45°.

Draw ∠ABY with Y on the same side of AB as X such that ∠ABY=60°.

Let AX and BY intersect at C.

ABC is the required triangle.

Question: 5

Draw △ABC in which AC= 6 cm, ∠A=90° and ∠B=60°.

∠A+∠B+∠C=180°

Therefore ∠C=180°−60°−90°=30°

Solution:

Constructions Exercise 17.4 Question: 5

Steps of construction:

  • Draw a line segment AC = 6 cm.

  • Draw ∠ACX=30°.

  • Draw ∠CAY with Y on the same side of AC as X such that ∠CAY=90°.

  • Join CX and AY. Let these intersect at B.

ABC is the required triangle where angle ∠ABC=60°.

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