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This year marks my tenth year as a teacher of Maths. During that time, I've built up a bank of teaching resources and ideas which I want to share with others. I'll polish them up a bit before uploading them here. Some can be incorporated into lessons and others act as discussion points.

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The majority of posts are focused around Maths, but there are some which look at pedagogy and CPD which can be used in other subjects/settings. Search for lesson resources using the tags at the side. Pedagogy has it's own section.

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Resources can be used in educational settings, including private tuition.

Quadrilaterals from Isosceles Triangles

 
Solution
 
Let's explore this problem using case analysis.
 
Case 1: The isosceles triangles share a common base.
 

The lengths of the other sides now determine the type of quadrilateral produced. If the other sides are different in length, it produces a kite. You could argue that placing on triangle over the other would create a delta/arrowhead but I'll leave that for you to decide.
 
If the lengths are the same, then it produces a rhombus, though this requires the triangles to be equilateral, which is a special case of being isosceles. If the isosceles triangles are right angled and isosceles, then it produces a square.
 
Case 2: The  isosceles triangles share a common leg.
 
The triangles can form a parallelogram, unless they are equilateral, in which case they produce a rhombus. Another variation produces a kite.
 
Case 3: The base of one triangle is the leg of the other triangle.
 
 
By adjusting the lengths of one triangle, they can form a trapezium, like the left two in the diagram above. Alternatively, the triangles can form an irregular quadrilateral with no special properties.
 
 
 
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