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Example 1

Areas of two similar triangles are 144 sq.cm. and 81 sq.cm. If one side of the first triangle is 6 cm then find the corresponding side of the second triangle.

Solution :

= 4.5 c.m.

Example 2

The side of an equilateral triangle ABC is 5 cm. Find the length of the side of another equilateral D PQR whose area is four times area of D ABC.

Solution:

Since both triangles are equilateral they are similar.

Example 3

The corresponding sides of two similar triangles are 4 cm and 6 cm. Find the ratio of the areas of the triangles.

Solution:

Example 4

D ABC ~ D PQR such that l (seg.AB) : l (seg.PQ) that is 8 : 6. If area of D ABC is 48 sq.cm what is the area of the smaller triangle.

Solution:

Example 5

In a trapezium ABCD, side AB çç CD. The diagonals AC and BD cut each other at M.

Prove that

Solution:

To Prove that

Consider D AMB and D CMD.

Ð AMB @ Ð CMD, vertical angles

Ð BAM @ Ð DCM alternate angles

\ By AA test D AMB ~ D CMD \

 

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[next page]

Index

5.1 Introduction
5.2 Ratio And Proportionality
5.3 Similar Polygons
5.4 Basic Proportionality Theorem
5.5 Angle Bisector Theorem
5.6 Similar Triangles
5.7 Properties Of Similar Triangles

Chapter 6

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