## Similar Triangles

### two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Similar triangles are triangles that have the same shape although their sizes are different. This means that their corresponding angles are equal, and their corresponding sides are proportional in length. Two triangles are said to be similar if and only if:

1. Their corresponding angles are congruent.

2. The ratios of their corresponding sides are equal.

If two triangles are similar, then one triangle can be considered as an enlargement or reduction of the other triangle. This means that if we know the length of one side of a triangle and the ratios of the other sides, we can find the lengths of the corresponding sides of the similar triangle.

The ratio of the corresponding sides of two similar triangles is called the scale factor. For example, if Triangle A is similar to Triangle B, then the scale factor can be written as:

scale factor = AB/DE = AC/DF = BC/EF

where AB, AC, and BC are the sides of Triangle A and DE, DF, and EF are the corresponding sides of Triangle B.

There are many real-life applications of similar triangles, such as in map making, construction, and engineering. By using similar triangles, architects and engineers can design buildings and structures that are both efficient and aesthetically pleasing. Additionally, similar triangles can be used to calculate distances and heights that are difficult or impossible to measure directly.

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