Name___________________________________
(Worth a Test Grade)
Part I: Definitions (2 points each)
Match each vocabulary word with its proper definition.
Geometry Chapter 3 Project
1) _____altitude
2) _____angle bisector
3) _____center of gravity
4) _____centroid
5) _____circumcenter
6) _____circumscribed
7) _____distance
8) _____incenter
9) _____inscribed
10) _____median
11) _____midsegment
12) _____orthocenter
13) _____parallel lines
14) _____perpendicular bisector
15) _____point of concurrency
16) _____segment bisector
A. the point of intersection of three or
more lines
B. the point of concurrency for three angle
bisectors
C. the point of concurrency for three
perpendicular bisectors
D. the point of concurrency for the three
altitudes
E. a circle passes through each vertex of
the polygon
F. a circle touches each side of the
polygon at exactly one point
G. the point of concurrency of the three
medians
H. balancing point of a triangle
I. a line, ray, or segment in a plane that
passes through the midpoint of a
segment
J. a bisector that is also perpendicular to
the segment
K. segment connecting the vertex of a
triangle to the midpoint of the opposite
side
L. segment that connects the midpoints of
two sides of a triangle
M. the length of the perpendicular segment
from the point to the line
N. perpendicular segment from a vertex to
the opposite side or to a line containing
the opposite side.
O. a ray that divides an angle into two
congruent angles
P. lines in the same plane that do not
intersect
Part II: Conjectures & Properties List (2 points each)
Below is the list of conjectures and properties that we have filled in throughout Chapter 3. Your
job is to look back in your notes as well as your book to create a more organized list of
conjectures. Fill in each conjecture and property with the appropriate word(s).
1) Perpendicular Bisector Conjecture – If a point is on the perpendicular bisector of a
segment, then it is ____________________ from the endpoints.
2) Converse of the Perpendicular Bisector Conjecture – If a point is equidistant from the
endpoints, then it is on the ___________________________ of the segment.
3) Shortest Distance Conjecture – The shortest distance from a point to a line is measured
along the ___________________________ from the point to the line.
4) Angle Bisector Conjecture – If a point is on the bisector of an angle, then it is
__________________ from the sides of the angle.
5) Angle Bisector Concurrency Conjecture – The three angle bisectors of a triangle are
_____________________________.
6) Perpendicular Bisector Concurrency Conjecture – The three perpendicular bisectors of a
triangle are _____________________________.
7) Altitude Concurrency Conjecture – The three altitudes (or lines containing the altitudes) of
a triangle are ______________________________.
8) Circumcenter Conjecture – The circumcenter of a triangle is _____________________.
9) Incenter Conjecture – The incenter of a triangle is _____________________________.
10) Median Concurrency Conjecture – The three medians of a triangle are ____________.
11) Centroid Conjecture – The centroid of a triangle divides each median into two parts so that
the distance from the centroid to the vertex is ___________ the distance from the centroid to
the midpoint of the opposite side.
12) Center of Gravity Conjecture – The __________________ of a triangle is the center of
gravity of the triangular region.
Part III: Slope (5 points each) Show all your work for full credit!
#1) One line passes through the points (–1, –2) and (1, 2); another line passes through the points
(–2, 0) and (0, 4). Are these lines parallel, perpendicular, or neither?
#2) One line passes through the points (0, –4) and (–1, –7); another line passes through the points
(3, 0) and (–3, 2). Are these lines parallel, perpendicular, or neither?
#3) One line passes through the points (–4, 2) and (0, 3); another line passes through the points
(–3, –2) and (3, 2). Are these lines parallel, perpendicular, or neither?
Part IV: Sketching (5 points each)
#1) SKETCH 3 angle bisectors and LABEL the point of concurrency with its proper name.
#2) SKETCH 3 perpendicular bisectors and LABEL the point of concurrency with its proper name.
#3) SKETCH 3 medians and LABEL the point of concurrency with its proper name.
Part V: Solving (3 points each)
#1) Point P is the centroid of the triangle. Use the Centroid Conjecture to find the missing lengths.
(3 points each)
B
J
BP = 16 cm
PK = 10 cm
CJ = 21 cm
K
AP = ______ cm
P
JP = ______ cm
A
L
C
CP =______ cm
PL = ______ cm
Chapter Three Constructions Project Rubric
Rubric must be handed in with project for full credit on project.
Project is due December 3rd (B Day) or December 4th (A day).
Projects can be handed in before Thanksgiving break with parent signature for 5 points extra.
Any project handed in late will lose 10 points for each calendar day. A project that is 2 days late
cannot earn higher than an 80. A project that is one full week late cannot earn higher than a 30.
Name: _____________________________ Block#: _________ Date handed in: _____________
Part I: 2 points each up to 32 points:
_____________
Part II: 2 points each up to 24 points:
_____________
Part III: 5 points each up to 15 points:
(3 points for the work and 2 points for the correct answer)
_____________
Part IV: 5 points each up to 15 points:
(3 points for the work and 2 points for the point of concurrency)
_____________
Part V: 3 points each up to 12 points:
(2 points for the work and 1 point for the correct answer)
_____________
Rubric attached: 5 points
_____________
Total: out of 100 possible points
_____________
Parent Signature here: ________________________