# Construction of Reflection over Two Parallel Lines

- Author:
- Melissa Hertel

- Topic:
- Straight Lines, Reflection

Please complete the instructions
Reflections over Two Parallel Lines
In this investigation, you’ll see what happens when you reflect a figure over a line then reflect the image over a second line parallel to the first.
when creating your polygon remember to click on your first point to finish thepolygon.
1. Open a Geogebra document
2. Construct any irregular polygon
3. Construct line EF
4. Reflect your polygon over line EF.
5. Consruct point G and a line through point G parallel to EF.
To construct a parallel line. special line tools, select parallel line. Then select point G then line EF.
6. Reflect the second image over line G
7. Drag the original figure and the two lines and observe their relationships to the two images
Question 1.
Two reflections move your orginal figure to its second image. What single transformation do you think will do the same thing?
Reflections over Two Parallel Lines (continued)
select the measurement tool then point A and A'', repeat for HI 8. Construct segment AA''
9. Construct points H and I where AA'' intersect the parallel lines
10. Measure AA'' and HI
Question 2
Drag one of the lines and compare the two distances (AA" and HI) how are they related?
Question 3
HI is the distance between the two lines. Why?
11. Translate the orginial figure by the vecotr A A". Select the transformation tool, translate object by vector select point A then A''.
Question 4
Describe the result of step 11, above. What single transformation is equivalent to the combination of two relections over parallel lines?
Question 5
Answer the following quuestions to explain why AA" and HI are related as they are:
a. How does AH compare to HA'?
b. How does A'I compare to IA'' ?
c. AA' + A'A" =
SAVE file as Lastname.2parallel
d. complete the rest of the explaination on your own.
geometer's sketchpad activity translated into Geogebra

save file as
lastname.intersecting