Vertical angles, as you will recall from high school Geometry, are the opposite angles that appear whenever two lines cross. Despite the name, vertical angles need not be vertically aligned. The image to the left has two pairs of vertical angles. My students are studying vertical angles, so I challenged them with the following question. |
How many pairs of vertical angles are in the diagram below? Spoiler Alert! Some students answered "three pairs," while others said "six." I asked students to justify their answers by listing the pairs of vertical angles. Students quickly found the three pairs below. I asked, "Did anyone find a fourth pair?" An intrepid student raised his hand. "Angles C X F and D X E." These vertical angles are harder to see, because of the extra line that runs through them. Students responded to his discovery with "ohhhh!!!" and a well-deserved round of applause. The final two pairs of vertical angles were then easy to find, bringing the total to six pairs of vertical angles in the diagram.
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Student imagination and communication are on display in the following activity that I give annually to my Geometry class at the beginning of the year. How do you get from using only these three rules?
One solution is Now imagine that there is a fourth rule, but you don't know what it is. All you know is that your friend used Rule 4 to get from Students came up with several suggestions for what the mystery rule could be.
How do we know what Rule 4 actually is? We need more data to test our three hypotheses! |
About Me
I started this blog to share my transformation from math nerd to math nerd who loves to share math with young people. I teach high school in Hanoi, Vietnam. Your comments are always welcome. Archives
May 2021
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