# Textbook

## Reference Books

1. Cabinet of mathematical curiosities - Ian Stewart
2. Cabinet of mathematical curiosities - Ian Stewart

# Teaching Outlines

## Concept #

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# =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.

1. 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
```
1. Understanding/ analysing the given problem
1. Identifying/ Naming the triangles
2. Identifying the sides whose length is not given
3. comparing two sides of triangles (visualising that 1st triangle is smaller than 2 nd triagle and viceversa
4. should identify the corresponding sides (sides having same allignment)
2. Procedure
1. find the ratio between the corresponding sides whose length is known $13/39=13*1/13*3=1/3$ 2. 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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