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Triangle Relations

Stage: 2 Challenge Level: Challenge Level:1

Inceeya from Glenarm College told us:

My solution is that the side of the isoceles triangle is the same length as the base of the equilateral triangle.

Well noticed, Inceeya. Yes, we could say that the sides of the equilateral triangle (which of course are all the same) are the same length as the shorter sides of the isosceles triangle.

Rhea from Mason Middle School compared the triangles very thoroughly. Here are some of the things she noticed:

1. They both have three sides/three angles.
2. Both have at least two acute angles.
3. All of their interior angles add up to 180 degrees.
4. These specific triangles have no 90 degree angles.
5. They are both 2D figures.
6. These two share the same area.

Some of these things would apply to any triangles - you might like to think about which ones - and some apply just to these two triangles. Rhea told us that she cut out both the triangles and put them next to each other to make her list. I am particularly impressed that Rhea suggests they have the same area. She explained how she worked this out:

I cut the equilateral triangle in half and saw if it would fit in the isosceles triangle. To my revelation it did. This is how I established that these two triangles have an equivalent area.

Excellent - thank you to Rhea and Inceeya.