**Chapter 4 Practical Geometry**

Question 1.

Construct a quadrilateral PQRS, given that QR = 4.5 cm, PS = 5.5 cm, RS = 5 cm and the diagonal PR = 5.5 cm and diagonal SQ = 7 cm.

Solution:

Construction:

Step I: Draw QR = 4.5 cm.

Step II: Draw an arc with centre R and radius 5 cm.

Step III: Draw another arc with centre Q and radius 7 cm to meet the previous arc at S.

Step IV: Join RS and QS.

Step V: Draw two arcs with centre S and R and radius 5.5 cm each to meet each other at P.

Step VI: Join RP, SP and PQ.

Thus PQRS is the required quadrilateral.

Question 2.

Construct a quadrilateral ABCD in which AB = 4 cm, BC = 3.5 cm, CD = 5 cm, AD = 5.5 cm and ∠B = 75°.

Solution:

Construction:

Step I: Draw AB = 4 cm.

Step II: Draw an angle of 75° at B and cut BC = 3.5 cm.

Step III: Draw an arc with centre C and radius 5 cm.

Step IV: Draw another arc with centre A and radius 5.5 cm to meet the previous arc at D.

Step V: Join CD and AD.

Thus ABCD is the required quadrilateral.

Question 3.

Construct a square whose side is 5 cm.

Solution:

Construction:

Step I: Draw AB = 5 cm.

Step II: Draw an angle of 90° at B and cut BC = 5 cm.

Step III: Draw two arcs with centre A and C and same radii of 5 cm which meet each other at D.

Step IV: Join AD and CD.

Thus, ABCD is the required square.

Question 4.

Construct a rhombus ABCD in which AB = 5.8 cm and AC = 7.5 cm.

Solution:

Construction:

Step I: Draw AB = 5.8 cm.

Step II: Draw an arc with centre B and radius 5.8 cm.

Step III: Draw another arc with centre A and radius 7.5 cm to meet the previous arc at C.

Step IV: Draw two arcs with centres A and C and of the same radius 5.8 cm to meet each other at D.

Step V: Join BC, AC, CD and AD.

Thus ABCD is the required rhombus.

Question 5.

Construct a rhombus whose diagonals are 6 cm and 8 cm.

Solution:

Construction:

Step I: Draw SQ = 8 cm.

Step II: Draw a right bisector of SQ at O.

Step III: Draw two arcs with centre O and radius 3 cm each to cut the right bisector at P and R.

Step TV: Join PQ, QR, RS and SP.

Thus PQRS is the required rhombus.

Question 6.

Construct a rectangle whose diagonal is 5 cm and the angle between the diagonal is 50°.

Solution:

Construction:

Step I: Draw AC = 5 cm.

Step II: Draw the right bisector of AC at O.

Step III: Draw an angle of 50° at O and product both sides.

Step IV: Draw two arcs with centre O and of the same radius 2.5 cm to cut at B and D.

Step V: Join AB, BC, CD and DA.

Thus, ABCD is the required rectangle.

Question 7.

Construct a quadrilateral ABCD in which BC = 4 cm, ∠B = 60°, ∠C = 135°, AB = 5 cm and ∠A = 90°.

Solution:

Construction:

Step I: Draw AB = 5 cm.

Step II: Draw the angle of 60° at B and cut BC = 4 cm.

Step III: Draw an angle of 135° at C and angle of 90° at A which meet each other at D.

Thus, ABCD is the required quadrilateral.

Question 8.

Construct a parallelogram ABCD in which AB = 5.5 cm, AC = 7 cm and BD = 8 cm.

Question 9.

Construct a rhombus PAIR, given that PA = 6 cm and angle ∠A = 110°.

Solution:

Since in a rhombus, all sides are equal, so PA = AI = IR = RP = 6 cm

Also, rhombus is a parallelogram

so, adjacent angle, ∠I = 180° – 110° = 70°