Students learn in geometry about lines drawn from a vertex of a triangle to the midpoint of the opposite side, lines drawn from a vertex perpendicular to the other side, etc. What we need to say is this. Lines are specified by two points. One point can be any vertex. The other can be a midpoint or a perpendicular. We can also define the line as drawn from a vertex, bisecting the angle. We just look at all the logical possibilities. Ask the students if they can think of another possibility. How about the line connecting midpoints of two sides?

 

The area of a rectangle is length times width. The area of a trapezoid is the altitude times the average of the two bases. The area of a triangle is the same as that of a trapezoid, just that one base is zero.

 

What is the definition of an isosceles triangle? Answer: A triangle with two sides equal. I ask them which two sides. This question confuses them, and compels them to think about the symmetry involved.