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

# Tag: angle

## Drop shadow II

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

## 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?

## 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.

## Outside the pentagon

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

## 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?

## The boomerang

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

## The pentagon proportion

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

## Baby steps

The edges of a cyclic quadrilateral extend to two intersections. O is the circle centre. The two diagonals intersect inside the circle. What is the angle α?

## The party hat II

An equilateral triangle with a circular arc through its red centre and two vertices. If the yellow area equals the green one, what’s the angle α?