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| Theorem 4 |
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| A perpendicular drawn from the right angle vertex of a right - angled triangle divides the triangle into two triangles similar to each other and also to the original triangle. |
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| ABC is a triangle right-angled at A. The perpendicular from A to BC meets BC at D. |
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(i)  |
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(ii)  |
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(iii)  |
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(iii)  can also be proved independently, as shown below. |
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