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**One Thought Forever**

“There is a close connection between getting up in the world and getting up in the morning.“

– Anon

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- Prove that the area of an equilateral triangle described on one side of a square is equal
- Prove that the area of an equilateral triangle described on a side of a right-angled isosceles triangle is half the area
- Prove that area of equilateral triangle on one side of a square is equal to half area of equilateral triangle on one of its diagonals.
- In Fig. 6.15, if Δ ABC ~ Δ DEF and their sides are of lengths (in cm) as marked along them, then find the lengths of the sides of each triangle.
- If one angle of a triangle is 60° and the other two angles are in the ratio 1 : 2, find the angles.

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