Prove that, given any three parallel lines, an equilateral triangle
always exists with one vertex on each of the three lines.
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?
We received two different approaches to the
solution. The first is based on what Stephanie from Beecroft School
Stephanie noticed that the large triangle is
made from four congruent triangles, one of which is the triangle
joining the midpoints. Stephanie therefore created the larger
triangle by making three copies of the smaller one and translated
and rotated them into place.
My question is:
How do you know the triangles are congruent?
Does the following diagram help?
Chip at King's Ely School and Eli sent in a
solution based on Stephanie's ideas.
Like my question above, I want to know how you
know the vertices of the larger triangle can be found in this way?
Also, if you can convince me you are right, how does the
construction to find the midpoint of the sides of the triangle work
The second approach involved parallel
How do you know the sides of the larger
triangle are parallel and how can you construct each of the lines
parallel to the sides of the original triangle. Why does the
Can you tell us more about how these
ideas work please?