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## Between the lines

Two coloured triangles share a vertex. Prove that the red line segments are parallel.

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A right isosceles triangle contains another triangle. What is the angle α? Advanced if no trigonometry is used.

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## The telescope

The odd regular polygons are stacked together, in increasing order, zigzagging to form a telescope that extends forever! What is the limiting angle (with respect to the horizontal) at which the telescope points?

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## The weight lifter

Express the x coordinate of E in terms of x coordinates of A, B, F, and G. The two black lines are supposed to be parallel to the x-axis.

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## Outside the pentagon

A regular pentagon and two coloured equilateral triangles. What is the angle α?

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## Baby block II

A square containing another square with an extended side. What is tan(α) in terms of the red and green segment lengths?

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## The boomerang

A quadrilateral and a triangle. What’s the angle α?

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## The pentagon proportion

A regular pentagon and a circular arc through its red centre. What’s the proportion α : β?

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