Triangles

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

A group activity using visualisation of squares and triangles.

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.

How can the school caretaker be sure that the tree would miss the school buildings if it fell?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Explore the triangles that can be made with seven sticks of the same length.

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

Weekly Problem 13 - 2012
The diagram shows contains some equal lengths. Can you work out one of the angles?