1. In the diagram below, , and
and
are drawn.
If and
, what is
?
(1)
(2)
(3)
(4)
2. If is mapped onto
after a line reflection and
is mapped onto
after a translation, the relationship between
and
is that they are always
(1) congruent and similar
(2) congruent but not similar
(3) similar but not congruent
(4) neither similar nor congruent
3. An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a
(1) cylinder with a diameter of
(2) cylinder with a diameter of
(3) cone with a diameter of
(4) cone with a diameter of
4. In regular hexagon shown below,
,
, and
all intersect at
.
When is reflected over
and then rotated
about point
,
is mapped onto
(1)
(2)
(3)
(4)
5. A right cylinder is cut perpendicular to its base. The shape of the cross section is a
(1) circle
(2) cylinder
(3) rectangle
(4) triangular prism
6. Yolanda is making a springboard to use for gymnastics. She has -inch-tall springs and wants to form a
angle with the base, as modeled in the diagram below.
To the nearest tenth of an inch, what will be the length of the springboard, ?
(1)
(2)
(3)
(4)
7. In the diagram below of right triangle , altitude
is drawn to hypotenuse
.
If ,
, and
, what is the length of
?
(1)
(2)
(3)
(4)
8. Rhombus has vertices
,
,
, and
. What is the perimeter of rhombus
?
(1)
(2)
(3)
(4)
9. In the diagram below of and
, angles
and
are right angles, and
.
If and
, what is the measure of angle
, to the nearest degree?
(1)
(2)
(3)
(4)
10. In the diagram below, ,
,
, and
are drawn such that
.
Which additional statement is sufficient to prove by AAS?
(1) and
bisect each other
(2) is the midpoint of
(3)
(4)
11. Which equation represents a line that is perpendicular to the line represented by ?
(1)
(2)
(3)
(4)
12. In the diagram of below, points
and
are on sides
and
repectively, such that
.
If is
more than
,
, and
, what is the length of
?
(1)
(2)
(3)
(4)
13. Quadrilateral has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral
is always true?
(1)
(2)
(3)
(4)
14. In the figure shown below, quadrilateral is circumscribed around circle
. The midpoint of
is
, and
.
If and
, what is the perimeter of quadrilateral
?
(1)
(2)
(3)
(4)
15. The coordinates of the endpoints of directed line segment are
and
. If
, the coordinates of
are
(1) ()
(2) ()
(3) ()
(4) ()
16. In triangle , points
and
are on sides
and
, respectively, such that
, and
.
If and
, what is the length of
, to the nearest tenth?
(1)
(2)
(3)
(4)
17. In the diagram below, rectangle has vertices whose coordinates are
,
,
, and
.
Which transformation will not carry the rectangle onto itself?
(1) a reflection over the line
(2) a reflection over the line
(3) a rotation of about the point (
)
(4) a rotation of about the point (
)
18. A circle with a diameter of cm and a central angle of
is drawn below.
What is the area, to the nearest tenth of a square centimeter, of the sector formed by the angle?
(1)
(2)
(3)
(4)
19. A child’s tent can be modeled as a pyramid with a square base whose sides measure inches and whose height measures
inches. What is the volume of the tent, to the nearest cubic foot?
(1)
(2)
(3)
(4)
20. In the accompanying diagram of right triangle , altitude
is drawn to hypotenuse
.
Which statement must always be true?
(1)
(2)
(3)
(4)
21. An equation of circle is
. The statement that best describes circle
is the
(1) center is () and is tangent to the
-axis
(2) center is () and is tangent to the
-axis
(3) center is () and is tangent to the
-axis
(4) center is () and is tangent to the
-axis
22. In ,
is the perpendicular bisector of
. Based upon this information, which statements below can be proven?
I. is a median.
II. bisects
.
III. is isosceles.
(1) I and II, only
(2) I and III, only
(3) II and III, only
(4) I, II, and III
23. Triangle has an area of
and a perimeter of
. If the triangle is dilated by a scale factor of
centered at the origin, what are the area and perimeter of its image, triangle
?
(1) area of and perimeter of
(2) area of and perimeter of
(3) area of and perimeter of
(4) area of and perimeter of
24. If , what is the value of
?
(1)
(2)
(3)
(4)