A question of help? Geometry?

Question

I get the conjectures but knowing how to apply em is different.
I complete the conjectures easily but looking at a whole new problem is so different. It's harder to apply which conjecture and ordering the terms that no conjecture is able to teach.

How can I learn to apply the conjectures given a problem and modling the problem to fit my satisfaction? What are some ways you learn it!


Besides, does the right brain use logic?

Answer 1

This is like getting to Carnagie Hall. Practice, practice, practice. Actually, you might want to look at the problem backwards. Say, "what can make this true"? Usually, you will come up with some answer you can work forward to.

As an example, suppose you are asked to prove the area of a trapezoid is the height x the average of the large and small base. You can look at the trapezoid and think of it as a rectangle and two triangles. You know the area of the rectangle= height x smaller base. You know the area of the two triangles 1/2(b1h)+1/2(b2h), where b1 and b2 are the excess length of the larger base broken into 2 parts.

Now you can envisage two more triangles, each congruent to one of the triangles formed previously. We can stick these on the trapezoid and form a larger rectangle= larger base x height. With no triangles, we have smaller basex height. With four triangles, we have larger base x height. The trapezoid consists of two triangles, so the area is halfway between these two rectangular areas.