Thales Essay, Research Paper

Thales Ship at Sea Activity – Thales ship at sea is a math activity saying that you can find the distance of something from where you are standing without actually measuring it. Thales “Ship at Sea” ActivityPurpose: The purpose of the activity was to learn that the Corresponding Partsof Congruent Triangles are Congruent (CPCTC), and how you can use it indifferent situations. We familiarized ourselves with the corresponding parts ofcongruent triangles. We also were supposed to find the distance to an object without actuallymeasuring the distance to that object directly. Step one: Suzie Pipperno and I had to pick a concrete block about forty feetaway from the sidewalk in back of the school.Step two: We then tried to align a cone with the cement block without gettingclose to it. Step three: We had to pace out a certain distance, 10 steps, from the cone,place a flag, the pace the same distance again, in a continuous segment, andplace another cone. Step four: We walked at a right angle to the second cone until we had the cementblock and the flag perfectly in line. Step five: We took a string and stretched it the distance from the second coneto the place we stopped walking. Step six: We placed the string against a tape measure and found that theapproximate distance from the cement block to the first cone was thirty eightfeet-two inches. Step seven: We used the string to measure the exact distance from the cementblock the first cone using the tape measure to measure the string, which wasforty two feet-one inch. Step Eight: We used the string to get an exact measurement from the first coneto the flag. Then used the string to correct the distance of the second conefrom the flag.Step nine: We walked at a right angle from the second cone until the flag andthe cement block are lined up again. Step ten: We used the string and tape measure to measure the distance of thepath we walked and came up with forty one feet-two inches. Conclusion: We were able to conclude, without directly measuring the distance to

the cement block, that the distance to the block was approximately forty onefeet-two inches. Relation: The way this activity relates to our mathematical studies is that itfamiliarizes us with the congruent parts of congruent triangles, and teaches usthat you can use the congruence of triangles in real life. How we proved the triangles congruent: If you look at the attached diagram youwill see that there are 2 sides with a | through them. That means that thosesides, or line segments, are congruent. You will also notice two angles with s spanning their angle measure. That means that that those two angles arecongruent. Also you will see two sides with a || through them. That means thesame thing as the first pair of segments with the | through them, but itsignifies that those two line segments are congruent with each other and not theother two. These triangles are congruent by a postulate SAS (Side-Angle-Side).Which states that if two triangles have a Side an Angle and a Side Congruentthen both of the triangles are totally congruent. Comments on Activity: I think that the activity was worthwhile, because Ilearned how errors in measurement and sighting can cause inaccuracies inmeasured distences, and the larger the distances you are working with, thelarger the errors. Idea to Improve or Extend: My idea is to do the activity three times, and ineach have the block at a different distance. This would enable you to see howdistance effects accuracy. GlossaryAngle- an angle consists of two different rays that have the same initial point,the vertex.Congruent angles- two angles that share the same measureCongruent segments- two segments that share the same measureCPCTC- abbreviation for corresponding parts of congruent triangles are congruentPostulate-A statement accepted without proof as trueSAS Postulate-If two sides and the included angle of one triangle are congruentto two sides and the included angle of another triangle, then the two trianglesare congruentTriangle- A polygon with three sides