Concept Byte: Paper Folding and Reflections

Use With Lesson 9-2

ACTIVITY

In Activity 1, you will see how a figure and its reflection image are related. In Activity 2, you will use these relationships to construct a reflection image.

Activity 1

• Step 1 Use a piece of tracing paper and a straightedge. Using less than half the page, draw a large, scalene triangle. Label its vertices A, B, and C.

• Step 2 Fold the paper so that your triangle is covered. Trace Δ A B C cap delta eh b c  using a straightedge.

  

• Step 3 Unfold the paper. Label the traced points corresponding to A, B, and C as A ′ , B ′ , and  C ′ , eh prime , comma , b prime , comma , and , c prime , comma  respectively. Δ A ′ B ′ C ′ cap delta , eh prime , b prime , c prime  is a reflection image of Δ A B C . cap delta eh b c .  The fold is the reflection line.

  

  

1. Use a ruler to draw A A ′ ¯ . eh , eh prime bar . .  Measure the perpendicular distances from A to the fold and from A ′ eh prime  to the fold. What do you notice?
2. Measure the angles formed by the fold and A A ′ ¯ . eh , eh prime bar . .
3. Repeat Questions 1 and 2 for B and B ′ b prime  and for C and C ′ . c prime , .  Then, make a conjecture: How is the reflection line related to the segment joining a point and its image?

Activity 2

• Step 1 On regular paper, draw a simple shape or design made of segments. Use less than half the page. Draw a reflection line near your figure.

• Step 2 Use a compass and straightedge to construct a perpendicular to the reflection line through one point of your drawing.

  
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4. Explain how you can use a compass and the perpendicular you drew to find the reflection image of the point you chose.
5. Connect the reflection images for several points of your shape and complete the image. Check the accuracy of the reflection image by folding the paper along the reflection line and holding it up to a light source.

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