Tamil Nadu Board Class 10 Solutions for Mathematics – Practical Geometry (English Medium)
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.
Ex 4.10 Construct a triangle similar to a given triangle PQR with its sides equal to of the corresponding sides of the triangle PQR (scale factor < 1).
Ex 4.11 Construct
a triangle similar to a given triangle PQR with its sides equal to
10. Construct
a triangle similar to a given triangle PQR with its sides equal to
11. Construct
a triangle similar to a given triangle LMN with its sides equal to
12. Construct
a triangle similar to a given triangle ABC with its sides equal to
13. Construct
a triangle similar to a given triangle PQR with its sides equal to of the corresponding sides of the triangle
PQR. (Scale factor
Example 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.
Example 4.18 : Construct a triangle ΔPQR such that QR=5cm, ÐP=30° and the altitude from P to QR is oflength 4.2 cm.
Ex 4.19 Draw a triangle ABC of base BC=8cm, ÐA=60° and the bisector of ÐA meets BC at D suchthat 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.
Example 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.
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.
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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