Thread: Similar Triangles: Error in course or understanding?

1. Similar Triangles: Error in course or understanding?

I'm have trouble with a particular problem in a Geometry course from The Great Courses. I've found other errors in the course and believe this is another but it's so egregious that I wanted to check to make sure I'm not just missing something. Please take a look at the problem below:

Question 10.i asks, Use similar triangles to show that

$\frac{y}{y+x} = \frac{s}{s+t}$

Shouldn't that be:

$\frac{x}{y+x} = \frac{s}{s+t}$

2. Re: Similar Triangles: Error in course or understanding?

Originally Posted by B9766

Question 10.i asks, Use similar triangles to show that
$\frac{y}{y+x} = \frac{s}{s+t}$
Shouldn't that be:
$\frac{x}{y+x} = \frac{s}{s+t}$
Actually it should be $\dfrac{y}{y+x} = \dfrac{t}{s+t}$
See that the 'sub-triangle' is similar to the 'super-triangle'.

3. Re: Similar Triangles: Error in course or understanding?

I would feel better about $\frac{y}{y+ x}= \frac{t}{s+ t}$ since y and t are sides of a triangle while x ad s are not so this follows directly from "similar triangles".

However, from $\frac{y}{y+ x}= \frac{t}{s+ t}$, we get $1- \frac{y}{y+ x}= 1- \frac{t}{s+ t}$ and then $\frac{y+ x- y}{y+ x}= \frac{s+ t- t}{s+ t}$ so $\frac{x}{x+y}= \frac{s}{s+ t}$ is also true.

4. Re: Similar Triangles: Error in course or understanding?

Thank you! I agree. I was so lost in segments and sub-segments I lost sight of the triangles.