Three squares and a regular pentagon. Prove that the three red vertices are collinear.
Categories
Staying in line
Tag: pentagon
Categories
Pentagon pleasure
Two regular pentagons. The centre of the large one is a vertex of the small one. What is yellow : green?
Categories
Pentagon divided
Given a pentagon ABCDE, construct the points T,R,Q,U such that the segments AT, AR, AQ, and AU divide the pentagon into five equal area pieces. (Using straight edge and compass. But you may divide a segment into a number of equal segments for free.)
Categories
Pentagon offspring
Three regular pentagons are placed as shown. Prove that the three black line segments are concurrent.
Categories
Playing fields
Show equality of the green and orange square playing field areas.
Categories
Folding a pentagon
One side of a regular pentagon is folded back and forth as shown. Are the six red line segments congruent?
Categories
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?
Categories
Outside the pentagon
A regular pentagon and two coloured equilateral triangles. What is the angle α?
Categories
The pentagon proportion
A regular pentagon and a circular arc through its red centre. What’s the proportion α : β?
Categories
The crosshairs
A regular pentagon and two semicircles. Prove that they are orthogonal, i.e. the tangents in the intersection point are orthogonal.