Oktay Mercimek, EMAT 6690
What we know about the reflection is the angle of incidence equals the angle of reflection. To demonstrate this property on the GSP, we need a Incoming ray first. Lets draw the ray and its extension which is in the same direction of the incoming ray, behind the mirror. Click "Show Step 1: First Circle" button. Please do not click a button unless you read the explanation for that step.
We know the segments |AH| and |DE| will be congruent when we construct them. Click "Show Step 2: Congruent Triangles" button. Did you see the similar triangles? Are they also isosceles triangles.
Our purpose in this construction is finding the appropriate angle for the
reflecting ray. To do that we need to know angle of reflection. It is clear that
angle of reflection is 
. Since Lines AE and HD
are intersecting each other at point B, we can say that
. Click "Show Step 3: Vertical Angles" button.
If we can find a point C on the upper side of the mirror such that
, construction will be complete.
Drawing a circle of radius |DE| and centered at point D will help us like the first circle. Click "Show Step 4: Second Circle" button.
It is clear that |DE|=|DC| (they are both radius.). Constructing segments DC
and BC will create triangle that is congruent to first triangles. Click "Show
Step 5: Third Triangle" button. Then we can see that
. "Show Step 6 Reflecting Ray"
button.
Actually we solved the problem with the last triangle. Ray BC is actually reflecting ray for the incoming ray AB. Click "Step 7 Hide Objects Except Reflecting" button.
Do you see another way to demonstrate reflection with circle?
Click Here to proceed Step 3: Parabola Reflection Page
Turn Back to Step 1: Parabola Construction Page