Similarity and congruence

problem

Bus Stop

Age

14 to 16

Challenge level

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4. The buses travel to and fro between the towns. What milestones are at Shipton and Veston?
problem

Points in Pairs

Age

14 to 16

Challenge level

Move the point P to see how P' moves. Then use your insights to calculate a missing length.
problem

Wedge on Wedge

Age

14 to 16

Challenge level

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?
problem

Is a Square a Rectangle?

Age

7 to 11

Challenge level

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
problem

Number the Sides

Age

7 to 11

Challenge level

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
problem

Pinhole Camera

Age

11 to 14

Challenge level

Make your own pinhole camera for safe observation of the sun, and find out how it works.
problem

Triangular Tantaliser

Age

11 to 14

Challenge level

Draw all the possible distinct triangles on a 4 × 4 dotty grid. Convince me that you have all possible triangles.
problem

Look Before You Leap

Age

14 to 16

Challenge level

Can you spot a cunning way to work out the missing length?
problem

A Shade Crossed

Age

14 to 16

Challenge level

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?
problem

ArRh!

Age

14 to 16

Challenge level

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?