There is more than one way to see that the yellow triangles must be
the same as the blue triangles if the blue triangles fit together as in
the diagram. For example, the red side on the yellow triangle
matches the red side on the blue triangle. The same is true for the
green side and the brown side. If two triangles have all 3 sides the
same then they must be the same triangle.
How can you be sure that the base of the top blue triangle will fit
exactly between the top points of the two lower triangles?
Where do you see parallel lines?
If the three angles in the blue triangle are a, b and c, what can
you say about the angles in the yellow triangle? How can you
be sure?
© MEI 2009
Teachers’ notes 1
Links to
•Proof
•Angles associated with parallel lines.
Possible questions to ask about the original
diagram:
• Where do you see parallel lines? How can you be
sure?
• Where do you see equal angles? How can you be
sure?
© MEI 2009
Teachers’ notes 2
•
•
If a row of blue triangles is placed on a horizontal base then the top
points must also be horizontal as the height of each triangle is the
same.
To be sure that the distance between these top points is equal to the
base of the blue triangle, you need to show that the yellow triangles
are the same as the blue ones. Knowing that the angles of a
triangle add up to 180° will show that the angles of the yellow one
are the same as the ones of the blue one. The two sloping sides of
the yellow triangle must also be the same as the sides of the blue
one. Does this guarantee that the triangles are the same?
© MEI 2009