### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Two Triangles

##### Age 11 to 14 ShortChallenge Level

In the diagram, triangle ABC is isosceles with AB = BC.

The line AP is drawn so that it meets the side BC at a right angle.

Prove that the angle marked $a$ is half the size of the angle marked $b$.

This problem is taken from 1000 Problems to Enjoy

You can find more short problems, arranged by curriculum topic, in our short problems collection.