Similarity and congruence

problem

Doubly Isosceles

Age

14 to 16

Challenge level

Find the missing distance in this diagram with two isosceles triangles
problem

Folding Squares

Age

14 to 16

Challenge level

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?
problem

Matter of Scale

Age

14 to 16

Challenge level

Can you prove Pythagoras' Theorem using enlargements and scale factors?
problem

Overlap

Age

14 to 16

Challenge level

A red square and a blue square overlap. Is the area of the overlap always the same?
problem

Folding Fractions

Age

14 to 16

Challenge level

What fractions can you divide the diagonal of a square into by simple folding?
problem

It Depends on Your Point of View!

Age

14 to 16

Challenge level

Anamorphic art is used to create intriguing illusions - can you work out how it is done?
problem

Triangular Slope

Age

14 to 16

Challenge level

Can you find the gradients of the lines that form a triangle?
problem

Pentakite

Age

14 to 18

Challenge level

Given a regular pentagon, can you find the distance between two non-adjacent vertices?
problem

Stadium Sightline

Age

14 to 18

Challenge level

How would you design the tiering of seats in a stadium so that all spectators have a good view?
problem

Chord

Age

16 to 18

Challenge level

Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.