Changes

Jump to navigation Jump to search
10,798 bytes added ,  15:36, 17 May 2017
m
Text replacement - "</mm>" to ""
Line 1: Line 1:  +
<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;">
 +
''[http://karnatakaeducation.org.in/KOER/index.php/ಅನುಪಾತ_ಮತ್ತು_ಸಮಾನುಪಾತ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
 
<!-- This portal was created using subst:box portal skeleton  -->
 
<!-- This portal was created using subst:box portal skeleton  -->
 
<!--        BANNER ACROSS TOP OF PAGE        -->
 
<!--        BANNER ACROSS TOP OF PAGE        -->
Line 20: Line 22:     
= Concept Map =
 
= Concept Map =
<mm>[[Ratio .mm]]</mm>
+
[[File:Ratio .mm]]
 
__FORCETOC__
 
__FORCETOC__
   Line 39: Line 41:  
===Notes for teachers===
 
===Notes for teachers===
 
For Solved Problems Click [http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion]
 
For Solved Problems Click [http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion]
 +
 +
[[http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion here]]
 +
 +
[http://www.mathsisfun.com Maths is Fun]
    
===Activity No # ===
 
===Activity No # ===
Line 111: Line 117:     
= Hints for difficult problems =
 
= Hints for difficult problems =
 +
==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.
 +
#Prerequisites: students should know the concept of similarity and proportionality
 +
        *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
 +
 +
# Understanding/ analysing the given problem
 +
## Identifying/ Naming the triangles
 +
## Identifying the sides whose length is not given
 +
## comparing two sides of triangles (visualising that 1st triangle is smaller than 2 nd triagle and viceversa
 +
## should identify the corresponding sides (sides having same allignment)
 +
#  Procedure
 +
## find the ratio between the corresponding sides whose length is known <math>13 / 39 = 13 * 1 / 13  *3 = 1/3</math>
 +
## express proportional corresponding sides (using the property of similarity)
 +
    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
 +
 +
Use the following Geogebra applet to understand proportion
 +
 +
<ggb_applet width="800" height="400" version="4.4" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
    
= Project Ideas =
 
= Project Ideas =
1,823

edits

Navigation menu