Triangle Reflection

Use the GeoGebra figure below to help answer the questions on your worksheet.
(Worksheet) The figure you are looking at is a red equilateral triangle (all sides the same length), and its reflection in green. Included on the figure is a movable point, and its corresponding point on the reflection’s triangle. Use the show/hide buttons and move the figure to help guide you through the following questions. Respond fully, answering all the questions and including anything you find interesting and/or relevant: Click and drag point b on the original triangle (red). What do you notice about point b’ (its reflection)? Do the same thing, but this time focus on the length of line BC. What happens to the lengths of the reflection’s sides when the original triangle is changed? Include some numeric examples (Ex.- Segment BC=___, Segment B’C’=____). What happens to point F’ (on the interior of the triangle) when F is moved? The radius of the circles centered on F and F’ are the distance to the corresponding point. Using the show/hide buttons you can see where these circles intersect. What do the intersections show us? What other points can we use to create similar intersections? There is a show/hide button for the segment connecting F and F’. How do you think this segment relates to the line of reflection (also a show/hide button)? Would you find similar relations with corresponding vertices (ex.- B and B’)?