1. Exploratory Challenge

Think back to Lesson 12 where you were asked to describe to your partner how to reflect a figure across a line. The greatest challenge in providing the description was using the precise vocabulary necessary for accurate results. Let’s explore the language that yields the results we are looking for.

Δ ABC is reflected across DE and maps onto Δ A'B'C'.

Use your compass and straightedge to construct the perpendicular bisector of each of the segments connecting A to A', B to B', and C to C'. What do you notice about these perpendicular bisectors? Label the point at which AA' intersects DE as point O. What is true about AO and A'O? How do you know this is true?

Draw your shapes on paper, take a picture, and upload them using the image upload icon .

If you do not have the ability to upload an image of your work type "Pictures are on paper."

Modified from EngageNY ©Great Minds Disclaimer

2. Construct the segment that represents the line of reflection for quadrilateral ABCD and its image A'B'C'D'.

What is true about each point on ABCD and its corresponding point on A'B'C'D' with respect to the line of reflection?

Draw your graph on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Graph is on paper."

Modified from EngageNY ©Great Minds Disclaimer

3. Construct the line of reflection across which each image below was reflected.

Draw your graph on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Graph is on paper."

Modified from EngageNY ©Great Minds Disclaimer

4. Construct the line of reflection across which each image below was reflected.

Draw your graph on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Graph is on paper."

Modified from EngageNY ©Great Minds Disclaimer

5. The task at hand is to construct the reflection of Δ ABC over DE. Follow the steps below to get started; then complete the construction on your own.

1. Construct circle A: center A, with radius such that the circle crosses DE at two points (labeled F and G).

2. Construct circle A: center F, radius FA and circle G: center G, radius GA. Label the (unlabeled) point of intersection between circles F and G as point A'. This is the reflection of vertex A across DE.

3. Repeat steps 1 and 2 for vertices B and C to locate B' and C'.

4. Connect A', B', C' to construct the reflected triangle.

Things to consider: When you found the line of reflection earlier, you did this by constructing perpendicular bisectors of segments joining two corresponding vertices. How does the reflection you constructed above relate to your earlier efforts at finding the line of reflection itself? Why did the construction above work?

Draw your graph on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Graph is on paper."

Modified from EngageNY ©Great Minds Disclaimer

6. Now try a slightly more complex figure. Reflect ABCD across EF.

Draw your graph on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Graph is on paper."

Modified from EngageNY ©Great Minds Disclaimer