Triangles Essay, Research Paper

Thales “Ship at Sea” Activity

Purpose: The purpose of the activity was to learn that the Corresponding Parts

of Congruent Triangles are Congruent (CPCTC), and how you can use it in

different situations. We familiarized ourselves with the corresponding parts of

congruent triangles.

We also were supposed to find the distance to an object without actually

measuring the distance to that object directly.

Step one: Suzie Pipperno and I had to pick a concrete block about forty feet

away from the sidewalk in back of the school.

Step two: We then tried to align a cone with the cement block without getting

close 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, and

place another cone.

Step four: We walked at a right angle to the second cone until we had the cement

block and the flag perfectly in line.

Step five: We took a string and stretched it the distance from the second cone

to the place we stopped walking.

Step six: We placed the string against a tape measure and found that the

approximate distance from the cement block to the first cone was thirty eight

feet-two inches.

Step seven: We used the string to measure the exact distance from the cement

block the first cone using the tape measure to measure the string, which was

forty two feet-one inch.

Step Eight: We used the string to get an exact measurement from the first cone

to the flag. Then used the string to correct the distance of the second cone

from the flag.

Step nine: We walked at a right angle from the second cone until the flag and

the cement block are lined up again.

Step ten: We used the string and tape measure to measure the distance of the

path 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 one

feet-two inches.

Relation: The way this activity relates to our mathematical studies is that it

familiarizes us with the congruent parts of congruent triangles, and teaches us

that you can use the congruence of triangles in real life.

How we proved the triangles congruent: If you look at the attached diagram you

will see that there are 2 sides with a | through them. That means that those

sides, or line segments, are congruent. You will also notice two angles with

?s spanning their angle measure. That means that that those two angles are

congruent. Also you will see two sides with a || through them. That means the

same thing as the first pair of segments with the | through them, but it

signifies that those two line segments are congruent with each other and not the

other 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 Congruent

then both of the triangles are totally congruent.

Comments on Activity: I think that the activity was worthwhile, because I

learned how errors in measurement and sighting can cause inaccuracies in

measured distences, and the larger the distances you are working with, the

larger the errors.

Idea to Improve or Extend: My idea is to do the activity three times, and in

each have the block at a different distance. This would enable you to see how

distance effects accuracy.

Glossary

Angle- an angle consists of two different rays that have the same initial point,

the vertex.

Congruent angles- two angles that share the same measure

Congruent segments- two segments that share the same measure

CPCTC- abbreviation for corresponding parts of congruent triangles are congruent

Postulate-A statement accepted without proof as true

SAS Postulate-If two sides and the included angle of one triangle are congruent

to two sides and the included angle of another triangle, then the two triangles

are congruent

Triangle- A polygon with three sides