STD-10 Chapter - 4 : PRACTICAL GEOMETRY - EX : 4.1 , 4.2 , 4.4

 

Tamil Nadu Board Class 10 Solutions for Mathematics –  Practical Geometry (English Medium)

STD 10 : CHAPTER: 4  PRACTICAL GEOMETRY English Medium Published By : P.Thirukumaresakani M.A.,M.Sc.,B.Ed., GGHSS, KONGANAPURAM, SALEM DT.

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         The study of Geometry is concerned with knowing properties of various shapes and structures. Arithmetic and Geometry were considered to be the two oldest branches of mathematics. Greeks held Geometry in high esteem and used its properties to discuss various scientific principles which otherwise would have been impossible. Eratosthenes used the similarity of circle to determine the circumference of the Earth, distances of the moon and the sun from the Earth, to a remarkable accuracy. Apart from these achievements, similarity is used to find width of rivers, height of trees and much more.

Eg 4.10 Construct a triangle similar to a given triangle PQR with its sides equal to (3/5) of the corresponding sides of the triangle PQR (scale factor (3/5) < 1).

Eg 4.11 Construct a triangle similar to a given triangle PQR with its sides equal to (7/4) of the corresponding sides of the triangle PQR (scale factor (7/4)  > 1).

EXERCISE - 4.1

 

10. Construct a triangle similar to a given triangle PQR with its sides equal to (2/3) of the corresponding sides of the triangle PQR. (Scale factor (2/3) <1).

11. Construct a triangle similar to a given triangle LMN with its sides equal to (4/5)  of the corresponding sides of the triangle LMN. (Scale factor (4/5)<1).

12. Construct a triangle similar to a given triangle ABC with its sides equal to (6/5) of the corresponding sides of the triangle ABC. (Scale factor (6/5) >1).

13. Construct a triangle similar to a given triangle PQR with its sides equal to (7/3) of the corresponding sides of the triangle PQR. (Scale factor   (7/3)>1).

Eg 4.17  : Construct a ΔPQR in which PQ=8cm, ÐR=60°and the median RG from R to PQ is 5.8cm.Find the length of the altitude from R to PQ.

Eg 4.18 :  Construct a triangle ΔPQR such that QR=5cm, ÐP=30° and the altitude from P to QR is oflength 4.2 cm.

Eg 4.19 Draw a triangle ABC of base BC=8cm, ÐA=60° and the bisector of ÐA meets BC at D such that BD=6cm.

EXERCISE - 4.2

11. Construct a ΔPQR which the base PQ=4.5cm, ÐR=35° and the median from R to RG is 6cm.

12. Construct a ΔPQR in which QR=5cm, ÐP=40° and the median PG from P to QR is 4.4cm. Find the length of the altitude from P to QR.

                    

13. Construct a ΔPQR such that QR=6.5cm, ÐP=60° and the altitude from P to QR is of length 4.5cm.

                  

14. Construct a ΔABC such that AB=5.5cm, ÐC=25° and the altitude from C to AB is 4cm.

                  

15. Draw a triangle ABC of base BC=5.6cm, ÐA=40° and the bisector of A meets BC at D such that CD=4cm.

             

16. Draw ΔPQR such that PQ=6.8cm, vertical angle is 50° and the bisector of the vertical angle meets the base at D where PD=5.2cm. 

               

Eg 4.31 :  Draw a circle of diameter 6cm from a point P, which is 8cm away from its center. Draw the two tangents PA and PB to the circle and measure their lengths.

EXERCISE - 4.3

14. Draw the two tangents form a point which is 10cm away from the centre of a a circle of radius 5cm.Also, measure the lengths of the tangents.

15. Take a point which is 11cm away from the centre of a circle of radius 4cm and draw the two tangents to the circle from that point.

16. Draw the two tangents from a point which is 5cm away from the centre of a circle of diameter 6cm. Also, measure the length of the tangents.

17. Draw the tangents to the circle from the point p having radius 3.6cm , and centre at 0. Point P is at a distance 7.2cm from the centre.

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