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Geometry Individual
KCATM
2006
Room #_________
USE CAPITAL LETTERS ON YOUR ANSWER SHEET
1) Which of the following best describes the following conditional statement:
If 5x2 = 10x then 5x = 10.
A)
B)
C)
D)
The statement is true because we can always divide both sides of an equation by x.
The statement is true because x = 2.
The statement is false because x = 0.
The converse of this statement is false because x = 0.
2) If two circles intersect at exactly one point, then the circles are said to be ______.
A) Concentric
C) Cocircular
B) Tangent
D) Crashing
3) Which angle is an acute angle (assume these diagrams are drawn to scale).
C)
A)
D)
B)
4) Suppose two cities are found on a map using a coordinate system. Lamont is located at (3, -6), Arlington is
located at (4, 5). A school is located at the midpoint between Lamont and Arlington. If each vertical or
horizontal unit on the map represents 0.75 miles, what is the approximate distance from Lamont to the
school?
A) 4 miles
B) 6 miles
C) 8 miles
D) 11 miles
5) What must occur for a conditional statement to be proven false.
A) A true hypothesis with a false conclusion.
B) A false hypothesis with a true conclusion.
C) A false hypothesis with a false conclusion.
D) None of these, conditional statements are never false.
6) Which statement is the Law of Syllogism?
A)
B)
C)
D)
is a true statement and p is true, then q is true.
is a true statement and q is true, then p is true.
and
are true statements, then
is a true statement.
and
are true statements, then
is a true statement.
If
If
if
If
7) Find the minimum distance between the lines 2x + 3y = 1 and 3x + 2y = 4
A)
B)
C)
D)
3 units
2.5 units
1.3 units
0 units
Page 1 of 7
Geometry Individual
KCATM
2006
Room #_________
USE CAPITAL LETTERS ON YOUR ANSWER SHEET
8) Which choice shows a conditional with the hypothesis and conclusion identified correctly?
A) If I throw the ball, then you will catch it.
Hypothesis: I throw the ball.
Conclusion: you will catch it.
B) Yesterday was Monday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Monday.
C) If I throw the ball, then you will catch it.
Hypothesis: I catch the ball.
Conclusion: You will throw it.
D) If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is Thursday.
9) The figure shown below is not drawn to scale. Suppose m∠AED = 82°. Which of the following statements is
false?
A)
B)
C)
D)
Not drawn to scale
m∠DEC = 98°.
BEC and CED are adjacent angles.
∠BEC is obtuse
AED and BEC are vertical angles.
10) Which angles are alternate exterior angles?
A)
B)
C)
D) none of these
11) Complete this statement. The sum of the measures of the interior angles of an n-gon is ____.
D) 180n
A) (n – 2)180
B) 360
C)
12) What is a correct name for the polygon?
A
B
E
A) EDCAB
C) CDEAB
B) ABCDA
D) BAEAB
C
D
Page 2 of 7
Geometry Individual
KCATM
2006
Room #_________
USE CAPITAL LETTERS ON YOUR ANSWER SHEET
13) Which figure is a polygon?
A)
B)
C)
D)
14) Complete this statement. A polygon whose sides all have the same length is said to be ____.
A) convex
B) equiangular
C) equilateral
D) regular
15) Write an equation in slope-intercept form, of the line through points (2, –4) and (1, 2).
A) y = –6x + 8
C) y = –6x + 4
B) y = 6x – 10
D) y = 6x – 16
16) Write an equation in slope-intercept form of the line through point P(–1, 1) with slope –5.
A) y = –5x – 4
C) y – 1 = –5(x + 1)
B) y – 1 = –5(x + 1)
D) y = –5x + 4
17) Is the line through points P(0, 5) and Q(–1, 6) parallel to the line through points R(3, 3) and S(5, –1)?
A) Yes
B) No
C) It is impossible to determine from the given information
18) Suppose the line containing points P(0, –9) and Q(2, –8) is perpendicular to the line containing points R(1,4)
and S(3, k). What is the value of k?
A) k = 0
B) k = 3
C) k = 5
D) It is impossible to determine from the given information
19) Write an equation in slope-intercept form of the line through points S(–10, –3) and T(–1, 1).
A)
C)
4
13
4
13
− x+
− x–
9
9
9
9
D)
B)
4
13
4
13
y= x+
y= x–
9
9
9
9
20) If
A)
, which of the following statements is true?
B) ∆MNO is isosceles C) ∆PQR is obtuse D)
21) The medians of a triangle intersect at a point called the __________?
A) orthocenter
B) microcenter
C) centroid
D) centrifuge
Page 3 of 7
Geometry Individual
KCATM
2006
Room #_________
USE CAPITAL LETTERS ON YOUR ANSWER SHEET
22) Which of the following lines is perpendicular to the line described by this equation: y = 5x +3?
A)
C)
y
y
8
6
6
4
4
2
–6
–4
2
–2
2
4
6
x
–8 –6 –4 –2
–2
–2
D)
y
6
4
4
2
2
2
–2
x
8
6
–2
8
–8
y
–4
6
–6
–6
–6
4
–4
–4
B)
2
4
6
x
–8 –6 –4 –2
–2
2
4
6
8
x
–4
–4
–6
–6
–8
23) In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?
A)
C)
B)
D)
Page 4 of 7
Geometry Individual
KCATM
2006
Room #_________
USE CAPITAL LETTERS ON YOUR ANSWER SHEET
24) Where can the perpendicular bisectors of the sides of a right triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A) I only
B) II only
C) I or II only
D) I, II, or II
25) Point T is the centroid of ∆PQR shown below. TP = 6.3 units. Find TM.
P
R
A) 2.10 units B) 3.15 units C) 3.65 units D) 5.25 units
T
M
Q
26) Name the largest angle of
The diagram is not to scale.
C
7
A
A)
B)
C)
D) It is impossible to determine from the side lengths
7
8
B
27) Which three lengths can NOT be the lengths of the sides of a triangle?
A) 23 m, 10 m, 14 m
B) 11 m, 10 m, 12 m
C) 5 m, 7 m, 8 m
D) 9 m, 20 m, 10 m
28) Two sides of a triangle have lengths 6 and 7. Which expression describes the length of the third side?
A) At least 13 units
C) Greater than 6 and less than 13 units
B) Greater than 1 and less than 13 units D) Greater than 1 and less than 7 units
29) Which statement is true?
A)
B)
C)
D)
All quadrilaterals are parallelograms.
All rectangles are rhombuses.
Some kites are parallelograms.
Some trapezoids are isosceles.
30) Which description does NOT guarantee that a trapezoid is isosceles?
A)
B)
C)
D)
congruent diagonals
both pairs of base angles congruent
diagonals bisect each other
the non-parallel sides are congruent
Page 5 of 7
Geometry Individual
KCATM
2006
Room #_________
USE CAPITAL LETTERS ON YOUR ANSWER SHEET
31) If,
a +b c +d
b
then
= ____.
=
b
d
a
B) b
A) a
b
c
C)
d
c
D)
d
a
32) The two rectangles are similar. Which equation can be used to find the correct value for x?
4m
8m
12 m
x
A) 32 = 16 + 2x
B) 12x = 32
C) 4 + x = 8 + 12 D) 16 + x = 28
33) Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.
x
5
A) 19.3
B) 11.1
C) 10.0
D) 8.7
20
34) Use the diagram.
AP?
C
is a diameter, and
9 cm
P
A
15 cm
. If CP = 9 cm and PB = 15 cm, then what is the length of
A) 6 cm
B
B) 12cm
3 34 cm
27
cm
D)
5
C)
D
Page 6 of 7
Geometry Individual
KCATM
2006
Room #_________
USE CAPITAL LETTERS ON YOUR ANSWER SHEET
35) Find the measures of the indicated angles. Which statement is NOT true? (The figure is not drawn to scale.)
A) a = 53°
d
B) b = 116°
C) c = 74°
D) d = 37°
53°
O
a
c
b
36) Which of the following equations represent the graph of a circle that contains the points (-6, 2) and (-3, 5)?
A) (x + 3)2 + (y – 2)2 = 9
C) (x – 3)2 + (y + 2)2 = 18
B) (x – 3)2 + (y + 2)2 = 9
D) (x + 3)2 + (y – 2)2 = 18
37) The area of a regular polygon can be found using the following formula:
A=
ns 2
 180 
4 tan

 n 
where n is the number of sides s is the length of each side, and the angle units are in degrees.
Which of the following values is equivalent to the area of a regular quadrilateral with side length of 5?
B) 5 2
C) 25
D) 25
A) 25 3
4
38) Which of the following choices best describes a possible transformation between the two triangles in the
graph?
y
4
A) A reflection in the y-axis
2
C) A translation on the vector <1, -1>
B) A translation on the vector <-5, 1> D) A translation on the vector <1, -3>
–4
–2
2
4
x
–2
–4
Page 7 of 7
# Correct
_________
# Incorrect
x4=
_________
Geometry Individual
Room Number: _____________
_________
x1=
-________
Score:
_________
Grade:
9
10
11
12
Name: ____________________
School: ___________________
Division (circle one):
1.
C
20.
D
2.
B
21.
C
3.
C
22.
B
4.
A
23.
B
5.
A
24.
D
6.
A
25.
B
7.
D
26.
B
8.
A
27.
D
9.
C
28.
B
10.
D
29.
D
11.
A
30.
C
12.
C
31.
C
13.
B
32.
A
14.
C
33.
B
15.
A
34.
D
16.
A
35.
B
17.
B
36.
A
18.
A
37.
D
19.
D
38.
B
Large
Page 8 of 7
Small
# Correct
_________
# Incorrect
x4=
_________
Geometry Individual
Room Number: _____________
_________
x1=
-________
Score:
_________
Grade:
9
10
11
12
Name: ____________________
School: ___________________
Division (circle one):
1.
20.
2.
21.
3.
22.
4.
23.
5.
24.
6.
25.
7.
26.
8.
27.
9.
28.
10.
29.
11.
30.
12.
31.
13.
32.
14.
33.
15.
34.
16.
35.
17.
36.
18.
37.
19.
38.
Large
Page 9 of 7
Small