Activity on Ratio proportion

==Ratio and Proportionality=

Exercise 2.4.2
In the adjacent figure, two triangles are similar. Find the length of the missing side This problem can be solved with the following steps. *Proportionality : two ratios are equal then four quantities are in proportional *Similar Triangles : If two triangles are said to be similar 1. if they are equiangular 2. the corresponding side are proportional
 * 1) Prerequisites: students should know the concept of similarity and proportionality

AC/DF = AB/DE 13/39 =  5/x 13 : 39 = 5 : x  (use the property of proportionality i.e Product of extremes is equal to product of means) 13 * x = 39 * 5 x = 39* 5 /13 x = 15 cms visualise and understand with geogebra applet <ggb_applet width="1366" height="550" version="4.4" 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 * 1) Understanding/ analysing the given problem
 * 2) Identifying/ Naming the triangles
 * 3) Identifying the sides whose lemgth is not given
 * 4) comparing two sides of triangles (visualising that 1st triangle is smaller than 2 nd triagle and viceversa
 * 5) should identify the corresponding sides (sides having same allignment)
 * 6)  Procedure
 * 7) find the ratio between the corresponding sides whose length is known $$13 / 39 = 13 * 1 / 13  *3 = 1/3$$
 * 8) express proportional corresponding sides (using the property of similarity)