Download 1. You want to prove that the perpendicular bisector of the base of

2009 FGCU Mathematics Competition.
Geometry Individual Test
1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is
also the angle bisector of the vertex. Which postulate/theorem can NOT be used in your
proof?
HL
SSS
SSA
SAS
2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures
three times the measure of angle A. If AC = 26, find AB.
13
13
26
(52/3)
13
3. In
ABC, AD = 8 and DB = 24. Find AC.
4
16
8
16
4
4. In right ABC, altitude
______ and ______.
is drawn to the hypotenuse. CD is the geometric mean of
AC and BC
AD and BD
AB and DB
AB and AD
5. In ABC,
is the altitude to side
make ABC a right triangle.
3
18
6
2
6
. If AD = 14 and DB = 4, find BC that will
6. In parallelogram ABCD,
______.
1
2. The reason for ABC and DEF being congruent is
SSA
AAS
SAS
ASA
7. Given:
QEL
DPC
Q
D
E
P
What must also be true?
DPC
QEL
QE
DP
E
D
C
L
All of the above
8. An equilateral triangle has ___________.
no congruent sides
only two congruent sides
all congruent sides
9. Given:
BSH
m B = 26
m S = 90
m H = 64
What is BSH?
an equiangular triangle
an acute triangle
a right triangle
an obtuse triangle
10. ___________ of a triangle is the angle adjacent to an interior angle of a triangle that is
formed when one of the sides of the triangle is extended.
An interior angle
A scalene
A complementary angle
A remote interior angle
An exterior angle
11. Which of the following statements is NOT true?
Q is the vertex of angles PQS, SQR, and PQR.
PQS and PQR are adjacent angles.
m PQR = m PQS + m SQR
T is in the interior of PQS.
P is in the exterior of RQS.
12. Points X and Y are on
. If AX > BY, then which statement must be true?
AY > BX
XY < BY
AY < BY
AY + BX > AB
AX < BX
13. Points E, F, and G are ______.
collinear
coplanar
noncoplanar
noncollinear
14. If two distinct planes intersect, they intersect in exactly ______.
one plane
one point
one line
two points
two lines
15. Which of the following statements is NOT true?
Planes X and Y contain both M and N.
Points N and P are noncoplanar.
Points L, M, N, and P are coplanar.
Plane Y and
intersect in point L.
16. The measure of each interior angle in a polygon is 120 . What is the name of the
polygon?
heptagon
quadrilateral
octagon
hexagon
decagon
17. Polygon G has k sides. How many diagonals can be drawn inside of polygon G?
k(k - 2) ÷ 2
3 (k - 2)
k(k - 2)
k(k - 3) ÷ 2
k(k - 2) ÷ 3
4 (k)
18. What is the sum of the measures of the interior angles of a pentagon?
1080
720
540
270
900
19. A statement whose truth is accepted without proof is considered to be a ___________.
Geometry
Definition
Point
Theorem
Postulate
20. A ___________ has position only. It does not have width, height, or length.
point
ray
space
rectangle
plane
21. How would you write that line segment PK has equal length with line segment OQ?
PK = OQ
PK = OQ
PK
OQ
PK = OQ
PK
OQ
22. Which of the following is not true?
The diagonals of a rhombus are congruent.
The diagonals of a rectangle are congruent.
The four sides of a rhombus are congruent.
A rectangle has 4 right angles.
A rhombus is a parallelogram.
The diagonals of a rhombus are perpendicular.
23. In ABC,
is the perpendicular bisector of
statement(s) must be true?
(I) ABD
ACD
(II) ABC is equilateral.
(III)
is the bisector of
and D lies on
. Which
BAC.
I and III only
II only
I only
III only
I, II, and III
24. Given:
D is in the interior of ABE.
E is in the interior of DBF.
F is in the interior of EBC.
m ABC = 150 , m EBC = 94 ,
m ABD = m EBF, m FBC = 2m
Which of the following is incorrect?
m
m
m
m
DBE
ABD = 18
ABF = 94
FBC = 76
DBF = 56
25. In ABC, k is the perpendicular bisector of side
following statements is incorrect?
and
=
. Which of the
Point D is the circumcenter of ABC.
ABC is a right triangle.
DAB
DBA
Point D is the incenter of ABC.
26. X is a point inside triangle ABC. If X is equidistant from
on the ______.
bisector of
C
perpendicular bisector of
median of C
altitude to side
and
, then X must lie
27. Triangle ABC is a 45°-45°-90° triangle with C at the right angle. If AC = 5, find BC.
10
5
5
10
5
28. In triangle ABC, the ratio of the measure of angle A to angle B is 1:3. The measure of
angle C is half the sum of the measures of angles A and B. If AC = 8, find BC.
4
8
4
4
8
29. Given circle O with segment AB tangent to the circle at A. If OA = AB, what kind of
triangle is OAB?
a scalene triangle
an isosceles right triangle
an equilateral triangle
an equilateral acute triangle
an isosceles obtuse triangle
30. In the figure, the radius for
statement is true?
P is r and the radius for
Circles P and Q have two common tangents.
PQ = R - r
PQ = R + r
Circles P and Q have four common tangents
Q is R. Which of the following