How To Use Mrs. Woodward's Theorem From Tangent To Yellow Wall

Mrs. Woodward has a lot of papers to give out to this class, so while the previous class works on their homework, she sorts the papers into piles for each students. She places the papers on each students desk as they walk in for class. She says she tries to always have their papers ready because handing them out wastes ten minutes of class time. This class took their benchmarks on Friday and apparently they did not do very well. She believes that it was a combination of not enough time mixed with a lack of preparedness. The students are not going to be happy when they see the grades. Once the students are all seated, Mrs. Woodward goes through what is in their pile of papers. The first paper is a warm-up and cool down sheet for the week. The second packet is a chapter 10 packet. There are a lot of terms and theorems in this chapter so she typed them up for …show more content…
The theorem states line ‘m’ is tangent to circle Q if and only if ‘m’ is perpendicular to QP. Because it states ‘if or only if’, the theorem works both ways. The students then get out their notebooks to do a few practice problems using this theorem. For the first two problems, the radius of the circe is given and they have to determine whether the segment show in tangent to the circle. To do this they have to prove the segment and the radius are perpendicular. They use the Pythagorean theory to show that angle ’t’ is a 90o angle, which proves that the lines are perpendicular and hence the segment is a target of the circle. The next two problems so how the theorem is applicable in the opposite direction. This time they can assume the segment is a target and must solve for the radius when given the other other sides of a triangle. Again, they use the Pythagorean theory to solve these problems. They do the first one together one the board and then they do the second problem independently at their desks before going over the answer as a