NAME: ____________________________
MS. KINZER
Project #1
DATE SUBMITTED: _____________
PERIOD ____
TRIANGLES: REAL-LIFE APPLICATION
DUE: TUESDAY, FEBRUARY 24, 2015
PART I. Urban Planning
A landscape planner is working on a blueprint for a new garden park in Long Island City, Queens. A diagram of
the plan is shown below.
a) A path will cut through the English garden so that it is the midsegment of the side of the garden that is
parallel to the horizontal axis. Find the coordinates of the endpoints of the midsegment and draw the
midsegment in the diagram above labeling the endpoints points A and B.
b) What is the length (in units) of the path that cuts through the English garden?
c) What is the slope of the path and the side of the garden it is parallel to?
d) The planner wants to place a bench at the circumcenter of the rose garden. Is this possible? Explain your
reasoning.
Part II. Construction
The part of a building that lies above ground is called the superstructure. One of the load-carrying
components of a superstructure is the truss. Trusses are supporting structures made of steel or wood that use
a triangular design. Trusses are used to span large distances and support very heavy loads. Bridges and roofs
are examples of structures that use trusses. One type of truss is shown in the diagram below.
a) If the base of the truss, 𝐴𝐺 = 24 𝑓𝑡, what is the midpoint of the truss and the length of ̅̅̅̅
𝐹𝐺 ?
b) Is point 𝐽 located on a perpendicular bisector? Explain.
̅̅̅ , ̅̅̅
̅̅ all have in common? Explain how can you support your claim?
c) What do ̅̅̅̅
𝐻𝐵 , 𝐼𝐶
𝐽𝐷, ̅̅̅̅
𝐾𝐸 , 𝑎𝑛𝑑 ̅̅
𝐿𝐹
̅̅̅ and 𝐾𝐸
̅̅̅̅ and 𝐿𝐹
̅̅̅̅ are both 3 feet, what are the lengths of 𝐼𝐶
̅̅̅̅ ?
d) If the lengths of 𝐻𝐵
e) Find the length of ̅̅̅
𝐴𝐽.
f) Suppose two beams, ̅̅̅̅̅
𝑀𝑁 and ̅̅̅̅
𝑂𝑃, are added to a portion of the truss to give it more support as shown
below. What are the lengths of the two new beams?
Part III. Monuments, Early Aircrafts, Birdbaths, Landscaping
a) You are building a monument in a triangular park. You want the monument to be the same distance from
each edge (side) of the park. Use the figure with incenter 𝐺 to determine how far from point 𝐷 you should
build the monument.
b) On many of the earliest airplanes, wires connected vertical posts to the edges of the wings, which were
wooden frames covered with cloth. The lengths of the wires from the top of a post to the edges of the frame
are the same and distances from the bottom of the post to the ends of the two wires are the same. What
does that tell you about the post and the section of frame between the ends of the wires?
c) Your neighbor is moving a new bird bath to his triangular backyard. He wants the bird bath to be the same
distance from each edge of the yard. Where should your neighbor place the bird bath? Explain.
d) You are planting a tree at the incenter of your triangular front yard. Use the diagram to determine how far
the tree is from the house.
TRIANGLES: REAL-LIFE APPLICATION PROJECT RUBRIC
CATEGORY
Complete Heading
All questions are answered and work is
neat. All numbers are written clearly.
Part I
a) Correct coordinates of the endpoints
of the midsegment are found and written
appropriately as two ordered pairs. An
accurate midsegment is drawn and
labeled with the assigned endpoints.
b) The correct length in units is found.
c) The correct slope is identified.
d) A valid explanation is given regarding
whether a bench can be placed at the
circumcenter of the rose garden.
Part II
a) A correct midpoint and length is found
for the given line segments.
b) A valid explanation is given whether
point J is in fact located on the
perpendicular bisector using given
supporting evidence.
c) A correct conclusion is made regarding
what the stated line segments have in
common as a result from the type of
segments they are.
d) Correct lengths are calculated for the
stated line segments.
Part III
Correct formulas are used to arrive at
correct answers for sections a, b, c, and d.
Clear, valid, and complete explanations
are provided where necessary. All work is
shown, step-by-step.
Project Submitted On Time
TOTAL
POINTS
POSSIBLE
3
12
28
28
28
1
100
POINTS
EARNED
COMMENTS