Question

prove lines are parallel
i can ensure that two lines are parallel by construction.
spark your learning
look at the optical illusion, known as the cafe wall illusion.
complete part a as a whole class. then complete parts b - d in small groups.
a. what is a question you can ask about the optical illusion? what information would you need to know to answer your question?
b. focus on two or three rows of the illusion. how does this help you answer your question?
c. to answer your question, what strategy and tool would you use along with all the information you have? what answer do you get?
d. how can you use tools to verify your answer?
turn and talk
. suppose all of the black squares are changed to white. how do you think changing the color would change the illusion? explain your reasoning.
. does turning the image so that the stripes are vertical change the illusion? what difference do you see, if any?

Explanation:

A. A possible question could be "Are the horizontal lines actually parallel?" Information needed would be the angles formed by transversals (if any) and the lines, or a way to measure the distance between the lines at multiple points.
B. Focusing on two - three rows helps in isolating a smaller, more manageable part of the illusion to check for parallelism. For example, one can look for consistent angles or distances between the lines in that section.
C. A strategy could be to use a straight - edge to check if the lines are parallel (by seeing if the straight - edge can be placed along the lines without gaps). A tool could be a protractor to measure angles. If the angles formed by a transversal and the lines are equal (corresponding, alternate interior etc.), the lines are parallel. The answer would be either that the lines are parallel or not based on the measurements.
D. Tools like a ruler to measure the distance between the lines at multiple points can verify the answer. If the distance is constant, the lines are parallel. For the "Turn and Talk" part: Changing the black squares to white might change the perception of the illusion as the contrast pattern is altered. Turning the image so that the stripes are vertical may change the illusion as our visual perception system processes vertical and horizontal patterns differently.

Answer:

A. Question: Are the horizontal lines actually parallel? Information: Angles formed by transversals or distance between lines at multiple points.
B. Helps in isolating a smaller section to check for parallelism by observing angles or distances.
C. Strategy: Use straight - edge. Tool: Protractor. Answer: Depends on angle/distance measurements.
D. Use a ruler to measure distances between lines.
Turn and Talk: Changing color may change the illusion due to contrast change. Turning vertical may change the illusion as visual perception of vertical/horizontal patterns differs.