Congruence Exploration 1 - Reflections in Parallel Lines

Work with a partner.

Draw a scalene triangle and label it triangle ABC. a. Draw any line DE. Reflect triangle ABC in line DE to form triangle A'B'C'. b. Draw a line parallel to line DE. Reflect triangle A'B'C' in the new line to form triangle A''B''C''.

c. Draw the line through point A that is perpendicular to line DE. What do you notice?

d. Find the distance between points A and A''. Find the distance between the two parallel lines. What do you notice?

e. Hide triangle A'B'C'. Is there a single transformation that maps triangle ABC to triangle A''B''C''? Explain.

f. Make conjecture (a statement that is true) based on your answers in parts (c)-(e). Test your conjectures by changing triangle ABC and the parallel lines.