Geometry Test Review
Write the name of the point of concurrency which corresponds to the given lines.
1. Perpendicular Bisectors _______________________
2. Angle Bisectors ____________________
3. Medians _______________________
4. Altitudes _______________________
Use a compass and straightedge to construct the following.
5. Construct a median of the triangle.
6. Construct an altitude in the triangle.
7. Construct the incenter of the triangle.
8. Construct a circumcircle around the triangle.
9. Given: AB ║ ED, C is the midpoint AD
Prove: AB  ED
A
B
C
E
D
10. Given: KL ║ MN, <K  <M
Prove: KN  LM
K
L
N
M
11. Given: AD and BC bisect each other.
Prove: AB║CD
D
B
E
A
C
12. Given: OM is the altitude to LN , OM is the median to LN .
Prove: <L  <N
O
L
M
N
13. Triangle ABC has vertices A(5, -3) B(-1, 7) and C(5, 5). Determine the point of
intersection of the medians, and state its coordinates. [The use of the set of axes below is
optional.]
14. Which geometric principle is used in the construction shown below?
1) The intersection of the angle bisectors of a
triangle is the center of the inscribed circle.
2) The intersection of the angle bisectors of a
triangle is the center of the circumscribed
circle.
3) The intersection of the perpendicular
bisectors of the sides of a triangle is the
center of the inscribed circle.
4) The intersection of the perpendicular
bisectors of the sides of a triangle is the
center of the circumscribed circle.
15. The diagram below shows the construction of the center of the circle circumscribed about
.
This construction represents how to find the intersection of
1) the angle bisectors of
2) the medians to the sides of
3) the altitudes to the sides of
4) the perpendicular bisectors of the sides of
1)
2)
3)
4)
16. For a triangle, which two points of concurrence could be located outside the triangle?
incenter and centroid
centroid and orthocenter
incenter and circumcenter
circumcenter and orthocenter
17. In the diagram below of
is 12 cm.
, medians
What is the length, in centimeters, of
1) 24
2) 12
3) 6
4) 4
18. In the diagram below of
If
1)
2)
3)
4)
, what is the length of
30
25
20
15
, and
intersect at G. The length of
?
, medians
?
,
,
, and
intersect at O.
19. In the diagram below, point P is the centroid of
If
1)
2)
3)
4)
and
, what is the length of
?
9
2
18
27
20. In the diagram below,
triangle PQR.
If
.
and
is a median of triangle PQR and point C is the centroid of
, determine and state the length of
.