At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

No Right Angle Here

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

A Sameness Surely

Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST and PU are perpendicular to AB produced. Show that ST + PU = AB

Terminology

Stage: 4 Challenge Level:
The green triangle is an isosceles triangle while the blue triangle is an equilateral triangle.

Find $a$ in terms of $b$ and $c$.

What can you say about the triangles if $a = b = c$?