Reflections

problem
Angular reflection

Age

11 to 14

Challenge level

Weekly Problem 28 - 2013
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?
problem
Symmetriangle

Age

11 to 14

Challenge level

Weekly Problem 35 - 2012
How many more triangles need to be shaded to make the pattern have a line of symmetry?
problem
Hidden meaning

Age

7 to 11

Challenge level

What is the missing symbol? Can you decode this in a similar way?
problem
Flipping twisty matrices

Age

14 to 18

Challenge level

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.
problem
Two triangles in a square

Age

14 to 16

Challenge level

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.
problem
Let us reflect

Age

7 to 11

Challenge level

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
problem
Transforming the letters

Age

7 to 11

Challenge level

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?
problem
Shady symmetry

Age

11 to 14

Challenge level

How many different symmetrical shapes can you make by shading triangles or squares?
problem
Reflecting squarely

Age

11 to 14

Challenge level

In how many ways can you fit all three pieces together to make shapes with line symmetry?
problem
Reflect again

Age

16 to 18

Challenge level

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.