The document RD Sharma Solutions - 17.4, Constructions, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.

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**Construct âˆ† ABC in which BC = 4 cm, âˆ B = 50Â° and âˆ C = 70Â°.**

Steps of construction:

- Draw a line segment BC of length 4 cm.
- Draw âˆ CBX such that âˆ CBX=50Â°.
- Draw âˆ BCY with Y on the same side of BC as X such that âˆ BCY = 70Â°Â°.
- Let CY and BX intersect at A.
- ABC is the required triangle.

**Draw âˆ† ABC in which BC = 8 cm, âˆ B = 50Â° and âˆ A = 50Â°.**

âˆ ABC+âˆ BCA+âˆ CAB=180Â°

âˆ BCA=180Â°âˆ’âˆ ABCâˆ’âˆ CAB

âˆ BCA=180Â°âˆ’100Â°=80Â°

Steps of construction:

- Draw a line segment BC of length 8 cm.
- Draw âˆ CBX such that âˆ CBX = 50Â°.
- Draw âˆ BCY with Y on the same side of BC as X such that âˆ BCY = 80Â°Â°.
- Let CY and BX intersect at A.

**Draw âˆ† PQR in which âˆ Q = 80Â°, âˆ R = 55Â° and QR = 4.5 cm. Draw the perpendicular bisector of side QR.**

Steps of construction:

- Draw a line segment QR = 4.5 cm.
- Draw âˆ RQX = 80Â° and âˆ QRY =55Â°.
- 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.

**Construct âˆ† ABC in which AB = 6.4 cm, âˆ A = 45Â° and âˆ B = 60Â°.**

Steps of construction:

- Draw a line segment AB = 6.4 cm.
- Draw âˆ BAX = 45Â°âˆ BAX = 45Â°.
- Draw âˆ ABY with Y on the same side of AB as X such that âˆ ABY = 60Â°Â°.

Let AX and BY intersect at C; ABC is the required triangle.

**Draw âˆ† ABC in which AC = 6 cm, âˆ A = 90Â° and âˆ B = 60Â°.**

We can see that âˆ A+âˆ B+âˆ C = 180Â°. Therefore âˆ C = 180Â°Â° âˆ’ 60Â°Â° âˆ’ 90Â°Â° = 30Â°.

Steps of construction:

- Draw a line segment AC = 6 cm.
- Draw âˆ ACX=30Â°.
- Draw âˆ CAY with Y on the same side of AC as X such that âˆ CAY = 90Â°Â°.
- Join CX and AY. Let these intersect at B.
- ABC is the required triangle where angle âˆ ABC = 60Â°