Honors Coordinate Alg / Geom Unit 7 Task 4 Review Worksheet
Name ______________________
Mark the sides/angles to indicate the parts made equal by the given lines.
1) circumcenter
2) incenter
3) centroid
4) orthocenter
What kind of line is being constructed in each of the following pictures?
5)
6)
7)
8)
What point is being constructed in each of the following pictures?
9)
10)
11)
12)
Complete the blanks with the following: altitude, angle bisector, median, and perpendicular bisector.
13) Every point of the __________________ is equidistant to the endpoints of a segment.
14) Every point on the _____________________ is equidistant to the sides of the angle.
15) A segment drawn perpendicular to a side of a triangle from the opposite vertex is called the _________________
16) A segment drawn to the midpoint of a side of a triangle from the opposite vertex is the _____________________
17) A line drawn perpendicular to a side of a triangle through its midpoint is the ______________________
18) A line or ray that bisects an angle is the _________________________
19) An entrepreneur owns 3 businesses on different streets in town and wishes to build an office building equidistant to
the 3 businesses. What lines does he need to construct to find the perfect site for his new building? ______________
20) Highway 140, Highway 5, and East Cherokee Drive form a triangle. An entrepreneur wants to build his new office
building equidistant to the 3 roads. What lines does he need to construct to find the perfect site for his new building? __
Honors Coordinate Alg / Geom Unit 7 Task 4 Review Worksheet
Name ______________________
Complete the blanks with the following: incenter, circumcenter, orthocenter, and centroid.
21) The 3 medians of a triangle meet at a point called ______________________.
22) The 3 perpendicular bisectors of a triangle meet at a point called ___________________________.
23) The 3 altitudes of a triangle meet at a point called __________________________.
24) The 3 angle bisectors of a triangle meet at a point called _____________________________.
25) The point that is equidistant to the sides of a triangle is called _________________________.
26) The point that is equidistant to the vertices of a triangle is called ________________________.
27) The center of gravity of a triangle can be found at the ___________________.
28) Birdy is designing a large triangular hang glider. She needs to locate the center of gravity of her glider. What point of
concurrency does she need to locate? ____________She also plans to decorate her hang glider with the largest possible
circle. What point of concurrency does she need to locate to use as the center of her large circle? ___________
29) The center of an inscribed circle is the _________________
30) The center of the circumscribed circle is the ___________________
31) The center of the inscribed triangle is the _________________________
32) The center of the circumscribed triangle is the _____________________
33) Suppose the cities of Waleska, Canton, and Ball Ground would like to construct a public swimming pool equally
accessible to all their citizens. What point of concurrency should the civil engineer use? _______________________
34) Bells Ferry Road, Highway 92, and Highway 5 form a triangle. Suppose the county wants to build a new hospital that
is equidistant to all 3 roads. What point of concurrency should they use? ___________________________________
Describe the location of the point of concurrency in each kind of triangle.
Point of Concurrency
Acute Triangle
Right Triangle
35) Incenter
36) Circumcenter
37) Centroid
38) Orthocenter
Obtuse Triangle
Honors Coordinate Alg / Geom Unit 7 Task 4 Review Worksheet
Complete the chart with circumcenter, incenter, centroid or orthocenter.
Fact
Name ______________________
P
Point U is called
T
39) UR = US
40) RQ = QP but <SQP is not a right angle. ST = TP
but <RTS is not a right angle.
41) PT = TS and RQ = QP and <RTP and <SQR are
right angles
42) <PSQ = <QSR and <PRT =
< SRT
43) RU = 2.UT and SU = 2UQ
S
U
Q
R
44) <PTR and <SQP are right angles and PT ≠TS
45) UQ = UT when they are the perpendicular
distances from point U to the segments PR and PS
F is the centroid of triangle ABD.
46) AC = 60. Find AF = ________ FC = ____________
47) BF = 60. Find EF = ________
48) EF = 60. Find EB = ________ BF = ___________
A
50) Find the ordered pair for the centroid.
(0, 1)
E
(7, -3)
F
49) DC = 60. Find CB = ________
(0, -7)
D
C
B
Name significant points or significant information!
51) Find the location of the centroid .
52) Find the location of the orthocenter.
A(0, -3) B(6, -1) C(-2, 5)
A(-6, -4) B(1, 10) C(7, 4)
53) Locate the circumcenter.
A(3, 2) B(3, -4) C(-1, -4)
Honors Coordinate Alg / Geom Unit 7 Task 4 Review Worksheet
Key:
Name ______________________
1) mark lines as perpendicular bisectors 2) mark angles as angle bisectors 3) mark lines as medians 4) mark lines
perpendicular to sides of triangle 5) angle bisector 6) altitude 7) perpendicular bisector 8) median
9) circumcenter 10) incenter 11) orthocenter 12) centroid 13) perpendicular bisector 14) angle bisector
15) altitude 16) median 17) perpendicular bisector 18) angle bisector 19) perpendicular bisector 20) angle bisector
21) centroid 22) circumcenter 23) orthocenter 24) incenter 26) incenter 26) circumcenter 27) centroid
28) centroid, incenter 29) incenter 30) circumcenter 31) circumcenter 32) incenter 33) circumcenter 34) incenter
35) inside any kind of triangle 36a) inside 36b) midpoint of hypotenuse 36c) outside by the longest side
37) inside any kind of triangle 38a) inside 38b) vertex of right angle 38c) outside by the obtuse angle
39) circumcenter 40) centroid 41) circumcenter
42) incenter
43) centroid
44) orthocenter
 4 1
 3 3
45) incenter
 11 17 
, 
3 3
46) AF = 40 FC = 20 47) 30 48) EB = 180 BF = 120 49) 60 50) ( 7/3, -3) 51)  ,  52) 
53) (1,-1)