Download Geometry Individual Test – January 2012 FAMAT

Geometry Individual Test – January 2012 FAMAT State-wide hosted by Vero Beach
NOTA = “None of the Above”
1) How many diagonals does a convex nonagon have?
A) 42
B) 30
C) 27
D) 20
E) NOTA
2) In Triangle BRH, BR = 10 meters, B  45 , and H  30 . Find the length of BH .
A) 10
B) 30
C) 5 2
D) 5 2  5 6
E) NOTA
3) Which of the following statements are true?
I. If the opposite sides of a polygon are parallel, this it is a parallelogram.
II. If the diagonals of a convex quadrilateral are congruent, then it is a rectangle.
III. If two lines are parallel, then their alternate exterior angles are supplementary.
A) I, II and III
D) I and II only
B) II and III only
E) NOTA
C) III only
4) In right triangle ABC, C is the right angle. If the measures of AB  4 and
AC  16   2 , find the sin A .
A)
1
2
B)

1
C)
1
4
D)

4
E) NOTA
5) Name the opposite rays found in the figure:
A) AB; CB
B) BA; CB
C) AB; BD
D) BA; BC
E) NOTA
6) One supplementary angle is four more than 7 times the measure of the other. Find the
measure of the smaller angle’s complement.
A) 78˚
B) 68˚
C) 58˚
7) What is the set of all points?
D) 18˚
E) NOTA
A) plane
D) line
E) NOTA
B) space
C) union
Geometry Individual Test – January 2012 FAMAT State-wide hosted by Vero Beach
8) A and F are complementary angles. R and A are supplementary angles. If F
and R are supplementary, what is the measure of A?
A) 30
B) 45
C) 60
D) 90
9) A regular polygon has an exterior angle equal to
E) NOTA
4
. What is the sum of the interior
a
angles of the polygon in terms of a?
4
4
4
A) 90a (180  ) B) 120a(180  ) C) 90a(180  a) D) a (180  )
a
a
a
E) NOTA
10) If the measure of 1  5 x  150 ; 2  7 x  48 , find the measure of angle 4.
A) 150˚
B) 170.5˚
C) 172.5˚
D) 175˚
E) NOTA
11) What is the height of a balloon from the ground during a wind storm that is on a 15 m
string and has an angle of elevation to the ground of 60 degrees? The balloon is tied to
the ground with a knot of negligible dimensions.
A)
15
2
B)
15 3
2
C)
15 3
6
D) 8
E) NOTA
12) Points A, B and C are collinear, in that order. Which of the following must be true?
I. AB + BC = AC
II. B is the midpoint of AC
III. A, B, C are coplanar.
A) I only
B) I and II only

D) I, II and III
E) NOTA
C) I and III only
13) In ABC, BAC is a right angle and AX is an altitude. If AX = 6 and XC = 8, what
is the perimeter of ABC?
A)
75
2
B) 36
C) 
30
D)

32
3
E) NOTA
Geometry Individual Test – January 2012 FAMAT State-wide hosted by Vero Beach
14) Which of the following is NOT a proper way to prove a quadrilateral is a
parallelogram?
A) Both pairs of opposite sides are parallel.
B) One pair of opposite sides are congruent and perpendicular.
C) Both pairs of opposite angles are congruent.
D) Both pairs of opposite sides are congruent.
E) NOTA
15) Find the radius of a circle with endpoints of its diameter at (-4, 5) and (-2, 7).
A)
2
B) 2 2
C) 10
10
2
E) NOTA
D) Equilateral
E)NOTA
D)
16) Identify the triangle with side lengths: 7, 12, 8.
A) Acute
B) Right
C) Obtuse
17) An octagon has exterior angles with measures: x + 5, 7x, 2x, x +55, 2x +7, x , 2x+20,
x+18. Find the smallest interior angle.
A) 76˚
B) 75˚
C) 61˚
D) 52˚
E) NOTA
18) Find the inverse of the following statement and its truth value:
If an angle is less than 90 degrees, it is an acute angle.
A) If an angle is acute, then it is less than 90 degrees. True
B) If an angle is acute, then it is less than 90 degrees. False
C) If an angle is not acute, then it is greater than or equal to 90 degrees. True
D) If an angle is greater than or equal to 90 degrees, then it is not an acute angle.
True
E) NOTA
19) Find the length of the midsegment parallel to the base of an isosceles triangle with
legs of length 50 units and a vertex angle bisector of length 14 units.
A) 24
B) 48
C) 96
D)140
E) NOTA
20) Find the height of a trapezoid with an area of 48 square centimeters and bases of 500
millimeters and 74 centimeters.
A)
23
cm
31
B)
24
cm
31
C) 7cm
D) 9cm
E) NOTA
Geometry Individual Test – January 2012 FAMAT State-wide hosted by Vero Beach
21) In USA , S is bisected by SY with Y on side UA . If all sides have integer values,
US  18 , and UY  12 ; find the smallest possible perimeter of USA .
A) 21
B) 24
C) 35
D) 45
E) NOTA
22) Brandi and Eric are standing atop two parallel posts that are 240 feet apart. Brandi’s
post has an altitude of 200 feet. Eric’s post has an altitude of 120 feet. Brandi really
wants to get to Eric, but she must touch the ground first. What is the shortest possible
distance between Brandi and Eric considering the width of the posts is negligible?
A) 400 feet
B) 415 feet
C) 450 feet
D) 500 feet E) NOTA
23) What is side length of a regular hexagon with an area equal to 144 3 square inches?
A) 6 6 in.
B) 4 2 in.
C) 4 6 in.
D) 24 6 in. E)NOTA
24) This number is prime, an odd integer, part of a Pythagorean Triple, and the number of
books in Euclid’s Elements.
A) 7
B) 8
C) 11
D) 13
E) NOTA
25) Find the negation and the truth value of:
If a polygon is a parallelogram, then it is a rectangle.
A) A polygon is not a parallelogram and it is not a rectangle. False
B) A polygon is a parallelogram and it is not a rectangle. False
C) A polygon is a parallelogram and it is not a rectangle. True
D) If it is not a rectangle, then it is not a parallelogram. False
E) NOTA
26) Find the equation of a perpendicular bisector of the diameter of the circle with
endpoints of its diameter at (-4, 5) and (-2, 7).
C) y  6  1( x  3)
D) y  6  x  3
E) NOTA
1
( x  3)
2
B) y  1( x  3)  6
A) y  6 
27) How many lines are determined by 6 points, no 3 of which are collinear?
A) 12
B) 14
C) 15
D)17
E)NOTA
Geometry Individual Test – January 2012 FAMAT State-wide hosted by Vero Beach
28) Using the figure above; GCO  FBO and BAO  ODH ,
mCOD   3x  12  , mBOA   7 x  86  . Find the measure of GCO .
A) 133.5˚
B) 130.5˚
C) 103.5˚
D) 93.5˚
29) Find the geometric mean of 140x 2 and 96x3 .
A) 8 x 2 210 x
B) 4 x 2 210 x
C) 70 x 2  48 x 3
30) If the scale factor of two similar triangle’s perimeters is
their altitudes?
3
4
A)
B)
4
3
C)
3
5
E) NOTA
D) 168x 2 x
E) NOTA
3
, what is the scale factor of
4
D) cannot be determined
E) NOTA