Download Points of Concurrency Construction Project Original

Points of Concurrency Construction Project Original by Mrs. Amanda Haynes
Using a compass and straight edge (ruler) you will construct the angle bisectors, perpendicular bisectors, altitudes,
and medians for 4 different triangles; a Right Triangle, Isosceles Triangle, Scalene Triangle, and an Equilateral
Triangle.
1.
Use the 4 triangles given out in class only for this project. You may print more triangles from the website
if needed. I suggest you use a pencil first and then go over the lines in the appropriate color. All lines
should be drawn with a straightedge.
2. Each triangle should be labeled ABC. (Black)
3. For every triangle, name the midpoint of AB point D, the midpoint of BC point E, and the midpoint of AC
point F. (Black)
4. Construct the 3 medians, 3 altitudes, 3 perpendicular bisectors, and 3 angle bisectors for each type of
triangle. Once each set of segments are found they should be colored as follows: angle bisectors – red,
perpendicular bisectors – blue, medians – green, altitude – purple.
5. All points of concurrency should be clearly marked and labeled for each triangle using the appropriate
color.
o Label the circumcenter of each triangle point Q.
o Label the incenter of each triangle point R.
o Label the centroid of each triangle point S.
o Label the orthocenter of each triangle point T.
6. All compass construction marks should be left on the paper in pencil.
7. All congruent segments and congruent angles should be clearly marked as well as any right angles.
8. In the “Description” section:
o Name and classify the triangle by angles and sides.
o Using complete sentences, describe the location of the points of concurrency (inside, on, or outside
the triangle).
9. The project should have a title page and be stapled together. Attach the rubric with a paper clip.
10. Answer the following questions once the project is completed: (write answers on attached rubric sheet)
a) The angles bisector of a triangle is (sometimes, always, or never) the perpendicular bisector.
b) The median of the triangle is (sometimes, always, or never) the perpendicular bisector.
c) The altitude of the triangle is (sometimes, always, or never) the perpendicular bisector.
d) The centroid of a triangle is (sometimes, always, or never) the circumcenter of the triangle.
e) The altitude from the vertex angle of an isosceles triangle is (sometime, always, or never) the
median.
f) The median of any side of an equilateral triangle is ( sometimes, always, or never) the angle
bisector.
g) The altitude of a triangle is (sometime, always, or never) the angle bisector of a triangle
h) The incenter of a triangle is (sometime, always, or never) the centroid of a triangle.
Honors Geometry
Points of Concurrency Project Rubric
Right Triangle
Acute Triangle
Name
Obtuse Triangle
Equilateral
Triangle
Correctly labeled ABC
Correctly labeled DEF
Correctly marked all congruent
segments
Correctly marked all congruent
angles
Correctly marked all right angles
Correctly constructed 3
perpendicular bisectors (3 points
each)
Correctly constructed 3 angle
bisectors (3 points each)
Correctly constructed 3 medians
(3 points each)
Correctly constructed 3
altitudes (3 points each)
Required colors used
Correctly labeled points of
concurrency
Correctly classified triangle by
its sides
Correctly classified triangle by
its angles
Correctly described points of
concurrency
Title Page (4 points)
QUESTIONS: (1 point each)
a)
_________________
b)
_________________
c)
_________________
d)
_________________
e)
_________________
f)
_________________
g)
_________________
h)
_________________
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