Angles, Polygons and Geometrical Proof Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Angles, Polygons and Geometrical Proof Age 11-14 and Age 14-16.

Printable worksheets containing selections of these problems are available here:

Stage 3 ★ Sheet 1 Solutions
  Sheet 2 Solutions
  Sheet 3 Solutions
  Sheet 4 Solutions
     
Stage 3 ★★ Sheet 1 Solutions
  Sheet 2 Solutions
  Sheet 3 Solutions
     
Stage 4 ★★ Sheet 1 Solutions
  Sheet 2 Solutions
     
Stage 4 ★★★ Sheet 1 Solutions


Folded Square

Age 14 to 16 Short Challenge Level:

This square piece of paper has been folded and creased. Where does the crease meet the side AD?

Cut-up Square

Age 14 to 16 Short Challenge Level:

Weekly Problem 15 - 2015
In the diagram, two lines have been drawn in a square. What is the ratio of the areas marked?

Triangular Intersection

Age 14 to 16 Short Challenge Level:

What is the largest number of intersection points that a triangle and a quadrilateral can have?

Height and Sides

Age 14 to 16 Short Challenge Level:

Can you find the area of the triangle from its height and two sides?

Circular Inscription

Age 14 to 16 Short Challenge Level:

In the diagram, the radius of the circle is equal to the length AB. Can you find the size of angle ACB?