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PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoLet us learn a few results on the similarity of triangles.
1. ![8.png](https://resources.cdn.yaclass.in/0bbc8dc6-b09f-4564-af10-d7aa9b8b3ef7/8w300.png)
![8.png](https://resources.cdn.yaclass.in/0bbc8dc6-b09f-4564-af10-d7aa9b8b3ef7/8w300.png)
A perpendicular line drawn from the vertex of a right-angled triangle divides the triangle into two similar triangles and the original triangle.
Here, \(\triangle ADB \sim \triangle ADC\), \(\triangle BAC \sim \triangle BDA\), \(\triangle BAC \sim \triangle ADC\).
2. ![9.png](https://resources.cdn.yaclass.in/ee262dab-108f-42cb-b591-2369997a3e34/9w400.png)
![9.png](https://resources.cdn.yaclass.in/ee262dab-108f-42cb-b591-2369997a3e34/9w400.png)
If two triangles are similar, then the corresponding sides' ratio is equal to the ratio of their corresponding altitudes.
That is, \(\triangle ABC \sim \triangle PQR\), then \(\frac{AB}{PQ} = \frac{BC}{QR} = \frac{CA}{RP} = \frac{AD}{PS} = \frac{BE}{QT} = \frac{CF}{RU}\)
3. ![4.png](https://resources.cdn.yaclass.in/a5206fbb-be1f-4a43-ba52-93082999716c/4w400.png)
![4.png](https://resources.cdn.yaclass.in/a5206fbb-be1f-4a43-ba52-93082999716c/4w400.png)
If two triangles are similar, then the corresponding sides' ratio is equal to the ratio of the corresponding perimeters' ratio.
That is, \(\triangle ABC \sim \triangle XYZ\), then \(\frac{AB}{XY} = \frac{BC}{YZ} = \frac{CA}{ZX} = \frac{AB + BC + CA}{XY + YZ + ZX}\)
4. ![4.png](https://resources.cdn.yaclass.in/a5206fbb-be1f-4a43-ba52-93082999716c/4w400.png)
![4.png](https://resources.cdn.yaclass.in/a5206fbb-be1f-4a43-ba52-93082999716c/4w400.png)
The ratio of the area of two similar triangles equals the ratio of the squares of their corresponding sides.
That is, \(\frac{ar(\triangle ABC)}{ar(\triangle XYZ)} = \frac{AB^2}{XY^2} = \frac{BC^2}{YZ^2} = \frac{CA^2}{ZX^2}\)
5. ![8.png](https://resources.cdn.yaclass.in/0bbc8dc6-b09f-4564-af10-d7aa9b8b3ef7/8w300.png)
![8.png](https://resources.cdn.yaclass.in/0bbc8dc6-b09f-4564-af10-d7aa9b8b3ef7/8w300.png)
If two triangles have a common vertex and their bases are on the same straight line, the ratio between their areas is equal to the ratio between the length of their bases.
That is, \(\frac{ar(\triangle ABD)}{ar(\triangle ADC)} = \frac{BD}{DC}\)