Exercise 17.4
Pages-17.6Question 1:
Construct ∆ ABC in which BC = 4 cm, ∠B = 50° and ∠C = 70°.
Answer 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.
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Question 2:
Draw ∆ ABC in which BC = 8 cm, ∠B = 50° and ∠A = 50°.
Answer 2:
∠ABC+∠BCA+∠CAB=180°∠BCA=180°-∠ABC-∠CAB∠BCA=180°-100°=80°
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.
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Question 3:
Draw ∆ PQR in which ∠Q = 80°, ∠R = 55° and QR = 4.5 cm. Draw the perpendicular bisector of side QR.
Answer 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.
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Question 4:
Construct ∆ ABC in which AB = 6.4 cm, ∠A = 45° and ∠B = 60°.
Answer 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°.

Question 5:
Draw ∆ ABC in which AC = 6 cm, ∠A = 90° and ∠B = 60°.
Answer 5:
We can see that ∠A+∠B+∠C = 180°. Therefore ∠C = 180° − 60° − 90° = 30°.
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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