**Q1: **

Simplify .

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**Q2: **

Simplify .

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**Q3: **

Simplify .

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**Q4: **

Simplify .

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**Q5: **

Simplify .

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**Q6: **

Simplify .

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**Q7: **

Simplify .

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**Q8: **

Simplify .

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**Q9: **

Simplify .

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**Q10: **

Simplify .

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**Q11: **

Using the relation , find an expression for in terms of and which holds when .

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**Q12: **

Using the relation , find an expression for in terms of and which holds when .

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**Q13: **

Simplify .

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**Q14: **

Simplify .

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**Q15: **

Simplify .

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**Q16: **

Simplify .

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**Q17: **

In the figure, which triangles are similar?

- A , , and
- B , , , and
- C , , and
- D , , , and
- E , , and

Given that , find expressions for the lengths of , , , and .

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- B , , ,
- C , , ,
- D , , ,
- E , , ,

Find an expression for .

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**Q18: **

Consider the given figure.

Find the lengths and in terms of and .

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- E ,

Find the lengths , , , and in terms of and .

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- B , , ,
- C , , ,
- D , , ,

By writing and in terms of , , , and , find expressions for and in terms of , , , and .

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- D ,

**Q19: **

In the given figure, is a rectangle and the length of is 1.

Find the lengths of and in terms of and .

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Find in terms of and . Hence find the lengths of and .

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By considering a suitable angle, find the lengths of and .

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Use your answers to the previous parts of the question to find expressions for and .

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