The proof of a theorem from geometry is dynamically being illustrated here.
Which theorem is it? And how does this applet informally illustrate its proof?
(Feel free to move the points anywhere you'd like!)
Theorem:
If 2 chords intersect inside a circle, then the product of the 2 segments of one chord = the product of the 2 segments of the other chord.
This applet shows it true. Here's how:
1) Both pink angles are congruent since they are 2 inscribed angles that intercept the same pink arc.
2) Both blue angles are congruent since they are 2 inscribed angles that intercept the same blue arc.
3) Thus, the two triangles shown are similar by AA~ Theorem.
4) Since corresponding sides of similar triangles are in proportion, we can write .
5) From this proportion, we can write , which proves the theorem.
