A problem with basic geometry.

[kenewbie]

I'm having problems figuring which sides of similar triangles correspond to each other. I can check and find the lines that go through the same angles, but that only works when they are constructed by crossing the same lines and similar approaches.

If you have a right triangle however, and divide it with a line from the 90 degree angle and down to the hypothenuse, you now have 3 triangles which are all similar. And I have to stare at these for 20 minutes and make miniature drawings to figure out which side corresponds to which in the other.

So, I'm thinking that I am missing some basic approach here, but I'm doing self study from a book so I can't kidnap a teacher and make him show me.

Any tips, or recommended reading?

k

 

[tiny-tim]

… concentrate on the angles …

Hi kenewbie!

Tip: concentrate on the angles, rather than the sides.

It's usually fairly easy to see which angles are the same.

For example, in your triple triangle, draw the triangle so that one angle is noticeably different from the other. So you have a small angle and a large angle, and you can easily tell which is which.

And then mark the pairs of identical angles with the same symbol … single dots for one pair, two dots for another pair, and so on (my favourite is little arcs instead of dots ).

Alternatively … again concentrating on the angles … carefully calculate what each angle is, and write it in … it's usually simple arithmetic.

So, in your triple triangle, going round clockwise, it's θ, 90º - θ, θ, 90º - θ, and back to θ!

(oh … and never make "miniature drawings" … make nice big ones! )