# Construction of Reflection over Intersecting Lines

Please complete the instructions
Reflections over Two Intersecting 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 that intersects 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 two intersecting lines (EF and GH) and their point of intersection (I)
4. reflect your polygon over line EF. Change the color of the reflected polygon. (See the figure below left. If necessary, move the polygon so that the image falls between the lines) steps 1-3
5. Reflect the second image over the second line, GH, change the color of the third figure. (see figure below right)
step 4 step 5
Reflections over Two Intersecting Lines (continued)
6. Drag the orginal 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?( If you are not sure, go on to the next steps, then come back to this question)
remember to click the right side of the angle then the left side of the angle to ensure you are measuring the interior and not exterior angle
7. Construct AI, where point A is a point of the orginal figure and point I is the point of intersection of the lines.
8. Construct IA' and IA'' dashed lines
remember you can move the measurements so it is easier to see and read 9. Measure < AIA''
10. Measure < EIH , the angle between the lines
Question 2
Compare the two angle measures. How are they related?
11. Select rotate Object around point by Angle. Select original object, then point I (center) and enter the angle measure you have for < AIA", in a clockwise direction.
Question 3
Describe the result of setp 11. What single trnasformation is equivalent to the combination of two reflections over intersecting lines?
Question 4
Answer the following questions to explain why m< AIA' and m< EIH are related the way they are
a. How does m< AIE compare to the m < AIA'?
b. How does m < A'IH compare to m<A'IA"?
c. m<AIA' + m<A'IA" = m< _____________
d. Complete the reset of the explanation on your own.

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