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
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
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
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.
Angle- an angle consists of two different rays that have the same initial point,
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
Triangle- A polygon with three sides