[code][/code]How can transformations such as reflections help us to learn more about familiar shapes? Consider reflecting a line segment (the portion of a line between two points) across a line that passes through one of its endpoints. An example of this would be reflecting [math]\overline{AB}[/math] across line [math]\overline{BC}[/math] in the picture below.

[b]Part A. [/b]Construct segment [math]\overline{AB}[/math] and line [math]\overline{BC}[/math] by using the segment [icon]/images/ggb/toolbar/mode_segment.png[/icon] and line [icon]/images/ggb/toolbar/mode_join.png[/icon] tools. Then create [math]\overline{A'B}[/math], the reflection of [math]\overline{AB}[/math], using the reflection tool [icon]/images/ggb/toolbar/mode_mirroratline.png[/icon]. Connect points A and A' with the segment tool. What figure is formed by points A, B, and A'? [br][br][i]Note: Point B might be covered by point B'[/i][br][br][b]Part B. [/b]Use what you know about reflections to make as many statements as you can about the shape formed in part (A). For example, are there any sides that must be the same length? Are there any angles that must be equal? Is there anything else special about this shape? Consider using the angle [icon]/images/ggb/toolbar/mode_angle.png[/icon] and distance [icon]/images/ggb/toolbar/mode_distance.png[/icon] measurement tools to conduct your investigation.