Buried Treasure Project- Due: _________________________________________________________
Target G4- I can prove and apply congruence theorems dealing with triangles to solve problems and justify my
solutions.
4
3
2
1
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In addition to being
proficient on the longterm target, I can
demonstrate one or
more of the
following…
Consistently utilize
efficient strategies to
accurately solve
problems in familiar
situations
Apply understanding
of long-term learning
targets to unfamiliar
situations and/or to
solve complex
problems
Use precise and
relevant
communication to
justify mathematical
thinking
Connect knowledge to
other learning targets
and/or advanced
problem sets.
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I can use a diagram that marks
the congruent segments and
angles and determine if two
triangles are congruent.
I can use a diagram that marks
the congruent segments and
angles and formally prove if two
triangles are congruent.
I can use Corresponding Parts
of Congruent Triangles
Theorem to determine and
prove other statements.
I can use theorems to justify
steps taken in finding missing
measures.
I can understand origins of points
of concurrency (Centroid,
Incenter, Circumcenter and
Orthocenter) of a triangle.
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I am beginning to and occasionally
demonstrate proficiency of one or more of
the following concepts… • Using a diagram
that marks the congruent segments and
angles and determining if two triangles are
congruent. • Using a diagram that marks the
congruent segments and angles and formally
proving if two triangles are congruent. •
Using Corresponding Parts of Congruent
Triangles Theorem to determine and prove
other statements. • Understanding the
origins of points of concurrency (Centroid,
Incenter, Circumcenter and Orthocenter) of
a triangle. • Using theorems to justify steps
taken in finding missing measures.
I have not completed the work necessary for
me to demonstrate proficiency
Your finished product should have:
 This paper- with answers to the questions (and for grading purposes)
 The original map with markings
 The map you created with markings
 Your story
1. Pirate Alphonse is standing at the edge of Westend Bay (at point A) and his cohort, Pirate
Beaumont, is 60 paces to the north at point B. Each pirate can see Captain Coldhart off in an
easterly direction burying his treasure. With his sextant, Alphonse measures the angle between
the captain and Beaumont and finds that it measures 48°. With his sextant , Beaumont measures
the angle between the captain and Alphonse and finds that it measures 80°. Alphonse and
Beaumont mark their positions with large boulders and return to their ship, confident that they
have enough information to return later and recover the treasure.
Can they recover the treasure? Which congruence theorem guarantees that they’ll be able
to find it? Explain. Use a protractor (or sextant) and ruler to locate the position of the treasure
on the map. Mark it with an X.
2. Captain Coldhart, convinced that someone in his crew stole his last treasure, has decided to
be more careful about burying his latest loot. He gives his trusted first mate, Dexter, two ropes,
the lengths of which only the captain knows. The captain instructs Dexter to mail one end of the
shorter rope to Hangman’s Tree (at point H) and to secure the longer rope through the eyes of
Skull Rock (at point S). The captain, with the ends of the two ropes in one hand and the treasure
chest tucked under the other arm, walks away from the shore to the point where the two ropes
become taut. He buries the treasure at the point where the two ropes come together, collects the
ropes, and returns confidently to his ship.
Has Captain Coldhart given himself enough information to recover the treasure? Which
congruence theorem ensures the uniqueness of the location? On your map, locate and mark the
position of this second treasure with a Y if the two ropes are 100 paces and 150 paces in length.
3. After the theft of two very important ropes from his locker and the subsequent disappearance
of his trusted first mate, Dexter, Captain Coldhart is determined that no one will find the
location of his latest buried treasure. The captain, with his new first mate Endersby, walks out
to Deadman’s Point (at point D). The captain, instructs his first mate to walk inland along a
straight path for a distance of 130 paces. There Endersby is to drive his sword into the ground
for a marker (at point M), turn and face the in the direction of the captain, turn at an arbitrary
angle to the left, continue to walk for another 60 paces, stop, and wait for the captain. The
captain measures the angle formed by the lines from Endersby to himself and from himself to
the sword. The angle measures 26°. The captain paces a boulder where he is standing (at point
D), walks around the bay to Endersby, and instructs him to bury the treasure at this point. Alas,
poor Endersby is buried with the treasure.
Has the captain given himself enough information to locate the treasure? If he has,
determine the unique location of the treasure and mark it with a Z. If he does not have enough
information, explain why not. How many possible locations for the treasure are there? Find
them on the map.
4. Now, make a map of your own. Identify necessary landmarks and write a story describing
how you could locate a place to bury- and later find- a treasure. Use one of the triangle
congruence theorems that you have not previously used. Make sure you state which triangle
congruence theorem you are using.