Acc. Geometry
Prac. Test No. 4 -HARD
1.
Name
Per/Sec.
Name a pair of perpendicular lines in the given
figure.
2.
Date
In the figure, " XYZ = " BAZ and " RST = " VUT
by AAS. " AZB = " RTS by ASA. m A = 6 x + 5 ,
m S = 45 , and m XZY = 2 x 2. Find the value of
m U + m V.
a) 1 1 5
b) 1 22
c) 1 3 0
d) 1 49
e) 1 66
$
$
$
$
$
a) AD and GI
b) AD and FK
c) EH and FK
d) EH and GI
e) not enough information is given
3.
Which figure does not contain a perpendicular
bisector?
a)
b)
c)
e) none of these
d)
4.
On a large machine, the centers of two pulleys
are 1 6 feet apart and the radius of each pulley
is 24 inches. How long a belt is needed to wrap
around both pulleys? (Find your answer to the
nearest tenth.)
a) 42.8 feet
b) 44.6 feet
c) 48.1 feet
d) 49.5 feet
e) 5 0.4 feet
Page 2
5.
In the diagram, " ABC = " XYZ by ASA with
AC = x + 1 3 and XZ = 3 x 7 , find the value of
AC + XZ.
a) 1 2
b) 1 7
6.
c) 2 6
d) 3 4 e) 48
7.
The shorter leg of a right triangle is 8 less than
the hypotenuse. The longer leg of the triangle
is one less than the hypotenuse. The perimeter
of the triangle is 3 0. What is the length of the
shorter leg?
a) 5
b) 6
c) 9
d) 1 2
8.
In the figure, m BGD = 1 44,
4 = 2 4, find m 5 .
m
a) 44
b) 5 2
d) 92
e) 1 2 0
m FGD = 68,
and
c) 7 6
Which triangle is
not acute?
a)
b)
c)
d)
e) 1 3
e)
9.
" ABC is a right triangle with a right angle at
vertex A . If AD is an altitude to the hypotenuse
with AB = 8 and m B = 3 0, find the length of BD.
a)
"
!
F
3
b)
&
!
F
3
c) 4
F
d) 4 3
F
e) 6 3
1 0.
" ABC is right with the right angle at vertex B
with BD an altitude to the hypotenuse. If DC = 7
and AD = 1 2 , find the degree measure of ABD to
the nearest degree.
a) 5 1 b) 5 3 c) 5 7 d) 65 e) 7 3 Page 3
1 1 . In the given diagram, if m * = 7 0 and m ) = 3 0,
find the degree measure of the exterior *+,.
1 2 . The given figure
then find the m
a) 7 0 b) 80 a) 2 2
b) 5 8
c) 90 d) 1 00 d) 1 2 3
e) 1 3 6
ABCD is a rectangle. If m
x.
1 = 68,
c) 1 08
e) 1 1 0 F
1 3 . A circle has a circumference of 3 . What is the
area of the circle?
a)
!
b)
!
"
c)
'
d)
'
"
1 5 . Which of the following best describes
I.
scalene
II.
isosceles
III.
right
IV.
obtuse
e) 3 " +,-.
1 4. In the figure, three lines intersect at a point. If
a = 42 , find the value of c.
a) 3 6
b) 42
d) 60
e) 90
1 6. Which triangle is acute and isosceles?
a)
b)
c)
d)
a) I only
b) IV only
c) I and III only
d) I and IV only
e) III and IV only
c) 48
e)
Page 4
1 7 . In the figure, the area of the square is 1 , find the
area of the shaded region.
a) 1 b) 1 c) 1 "
d) 1 + e) 1 + "
1 8. In the figure, two semicircles are drawn in a
square. If the length of the side of the square
is 4, what is the area of the shaded portion in the
figure?
a) 4
c) 8
e) 1 6
1 9. Given the following diagram with BA CD,
CB = DB, m C = 5 ( x 3 ), and m D = 2 x + 2 1 . Find
the value of m 1 + m 2 .
a) 3 6
b) 45
d) 82
e) 90
2 1 . Given that
m A = (2 x
a) 2 6 c) 60
c) 44 b) 8
d) 1 6
2
2
2 0. In the given figure, if s = 6 3 , find the value of q .
a) 4
c) 6 2
b) 6
d) 6 3
e) 8
A and B are complementary, if
3 ) and m B = (3 x + 8) , find m A.
b) 3 1 4
4
d) 5 9 e) 61 2 2 . Which triangle is not isosceles?
a)
b)
c)
d)
e)
Page 5
2 3 . Write a function A to determine the shaded area
of the given figure.
A ( x) = x 6 x 1 4
b) A ( x) = x + 8 x + 1 0
c) A ( x) = 2 x + 8
d) A ( x) = 2 x
4x 4
e) A ( x) = 2 x + 1 2 x 2
2 5 . In right ABC, m $ BAC = 3 0. If BC is extended
to D and AC is extended to E, then find the value
of e + d.
b) 1 2 0 c) 1 40
b) 3 1
c) 3 6 d) 3 7 " e) 3 7
2 7 . If the diagonals of a rhombus have lengths of 1 8
and 2 4, what is the length of the perimeter of the
rhombus?
b) 42
2 6. In the figure, ABC = CDA by Hypotenuse-Leg
with m $ BAC = 5 2 !" and m $ AEC = 3 x + # , find the
value of x.
a) 2 4
d) 1 45 e) 1 5 0
a) 1 5
OA
OC
b) OB OG
c) OD OF
d) OE OG
e) OG OA
a)
a)
a) 90
2 4. Which of the following pairs of rays are
perpendicular in the figure?
c) 48
d) 60
e) 2 1 6
2 8. If point P lies between points
of the following is true?
M lies on PN
b) N lies on PM
c) P lies on MN
d) MP + MN = NP
e) MN PM = PN + 2 MN
a)
M and N, then which
Page 6
2 9. In the figure, )* and ,+ the are the bases of
trapezoid ABCD , AD = 1 0 and CD = 1 2 . Find the
perimeter of the trapezoid.
3 0. All triangles shown in the drawing are equilateral
with DE = 3 . Find the perimeter of " )*+
F
a) 9
b) 9 3
c) 1 8
d) 1 8 3
F
e) 2 7
F
F
F
F
a) 5 ( 3 + 2 )
b) 41 ( 3 + 2 )
c) 3 9 + 5 5
d) 3 9 + 5 ( 3 + 2 )
F
F
F
F
F
e) 3 9 + 1 0(2 3 + 2 )
3 1 . A ramp 60 m long rises a vertical distance of 8 m.
Find the measure of the angle of elevation to the
nearest degree.
a) 3
b) 5
c) 8
d) 1 0
e) 1 2
3 3 . Given the figure, which inequality is true?
a)
c)
e)
RV > RS
ST > RV
RV < UT
UT < ST
d) SV < ST
b)
3 2 . All equiangular triangles are also
triangles.
a) obtuse
b) equilateral
d) scalene
e) right
c) isosceles
3 4. Given the two rectangles in the figure, find the
value of WX + YZ ?
F
F
a) 4 3
b) 6 3
c) 6 6
d) 1 8
F
F
e) 1 8 2
Page 7
3 6. In the figure, CD bisects ACB and AE bisects
CAB. Given m CDE = 5 0 and m CAE = 2 5 , find
the degree measure of B.
3 5 . Which triangle is acute and isosceles?
b)
a)
c)
a) 45 b) 60 c) 80 d) 1 00 e) 1 3 0 d)
e)
3 7 . In equilateral triangle ABC , D is the midpoint of
segment AB and AC = 1 2 . Find the length of CD.
a) 3 3
b) 4 6
c) 6 6
d) 4 3
e) 6 3
3 8. In the figure, ABC is inscribed in a semicircle
with area of 8 . What is the area of ABC ?
a) 4 b) $ !
c) d) e) It cannot be
determined from
the information
given.
"
3 9. In the figure FE and AC intersect at B with
BD
AC and BD bisects AC. If m DBE = 4 x
and m EBC = 6 x 2 , then find m ABF.
a) 1 0
b) 2 4
d) 46
e) 5 8
c) 3 2
8
&
!
40. In the given figure, if IJKL is an isosceles
trapezoid with bases LK and IJ. If m JKL = 7 1 and
m JLK = 42 , find m I.
a) 7 1
b) 89
c) 95
d) 1 09
e) 1 1 8
)??AI format version 3 .60B
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