# Ratio and Proportion

Philosophy of Mathematics |

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## Contents

# Concept Map

# Textbook

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# Additional Information

## Useful websites

## Reference Books

1. Cabinet of mathematical curiosities - Ian Stewart

2. Cabinet of mathematical curiosities - Ian Stewart

# Teaching Outlines

## Concept #

### Learning objectives

### Notes for teachers

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## Concept #

### Learning objectives

### Notes for teachers

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# 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 '"`UNIQ--postMath-00000001-QINU`"'
- 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

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