Download Geometry Semester Exam

Geometry Semester Exam
Some questions (c) 2013 by TEKS Resource System.
Some questions (c) 2012 by Region 10 Educational Service Center.
Page 2
GO ON
1
According to Euclidean geometry, the
points that lie on the same line are called
_____ points.
3
A linear
A There are no lines on the surface of
a sphere.
B collinear
C
In spherical geometry, two points do not
necessarily determine a line, as is the
case in Euclidean geometry. Which best
explains the reason why this is true?
non­collinear
B Points on a circle do not lie in the
same plane.
D congruent
C
2 In a geometric system, which would best
describe how postulates differ from
theorems?
F
Postulates do not require proof and
are presumed true, while theorems
are statements requiring proof.
G
Postulates are statements that
require proof, while theorems
cannot be proven.
On a sphere, two points can lie on an
infinite number of great circles.
D Lines in spherical geometry can only
be formed when great circles
intersect each other.
4
H Postulates do not require proof and
are known to be true, while
theorems may or may not be
proven to be true.
J
There is no difference between
postulates and theorems.
F
102°
G
36°
H 42°
J
Page 3
not enough information to find the
measure
GO ON
5
Danielle wants to translate triangle XYZ
so that vertex Y is moved from
coordinates (–4,2) to (0,­3). Which of
the following identifies the steps that can
be used to find the new coordinates of X
and Z?
7
Which congruence best expresses the
relationship showing that the triangles
below are congruent?
A Move each vertex 4 units left and 5
units up.
B Move each vertex 4 units right and
5 units down.
C
Move each vertex 4 units down and
5 units right.
D Move each vertex 4 units up and 5
units left.
A SSS
B SSA
C
SAS
D ASA
6 What information is needed to prove under AAS congruence?
8 The midpoint of is located at the
origin, and one endpoint of this segment
has coordinates of (8, ­10). What are the
coordinates of the other endpoint?
F
(­10, 8)
G
(­10, ­8)
H (­8, 10)
J
F
(­8, ­10)
No additional information is needed.
G
and bisect each other.
H
and are medians.
J
and are altitudes.
Page 4
GO ON
9 Points P (­3, ­2), Q (­1, 6), and R (5, 4)
define triangle PQR when placed on a
coordinate grid. What is the length of 11
The line below passes through the
points (­2, ­4) and (3, 5).
?
A
Which of these equations best
represents a line parallel to the line in
this graph?
B
C
10 units
A
D 14 units
B
C
10
Which of the following equations
represents a line perpendicular to the
graph of the equation F
D
?
G
H
J
Page 5
GO ON
12
On the number line, Point Q lies
between Point P and Point R. If the
distance between segment PR is 26
and PQ is 15, what is the distance
between segment QR?
14
In the graph below, what scale factor is
used to go from
to ?
F
G
H
J
13
Point B is between points A and C.
Which of the following is NOT true?
F. A, B, and C are collinear.
F
G. Ray AB is the same as Ray BA.
H 2
G
J
3
H. Ray AC is the same as Ray AB.
J. Ray BC and Ray BA are
opposite rays.
A F
B G
C
H
D J
15
A picture of a honeycomb can be drawn
by repeating a hexagon without
overlapping or leaving empy spaces.
Which of these would produce this
design?
A fractal
B tessellation
C
three­dimensional drawing
D dilation
Page 6
GO ON
16
As a project for geometry, students are
asked to make an enlarged copy of a 3
inch by 4 inch cartoon. They are asked
17
The measure of the central angle for
each of four regular polygons is shown
below.
to draw a inch by inch grid on the
cartoon, and then draw a 1 inch by 1
inch grid on a 12 by 16 inch poster
board. They are to copy the smaller
cartoon by duplicating the marks from
Which expression best represents the
measure in degrees of the central angle
of a regular polygon having n sides?
each inch square to its
corresponding 1 inch square on the
poster board. This is an example of
which transformation?
A
F
a translation
C
G
a rotation
B
D
H a reflection
J
a dilation
18
If line l is parallel to line m and line m is
NOT perpendicular to line n, which of
the following can be concluded?
F
Line n is perpendicular to line l
G
Line n is not parallel to line l
H Line n is parallel to line l
J
Page 7
Line n is not perpendicular to line l
GO ON
19
Given C is the midpoint of , and lines shows the steps of the proof of and are parallel. Which of the following
, in the correct logical order?
A
B
C
D
Page 8
GO ON
20
The table below shows triangles formed when all the diagonals are drawn from one vertex
in different regular polygons. Which of the following statements is true based on the
table?
F
All the triangles formed in each regular polygon are congruent.
G
All the triangles formed in each regular polygon are isosceles.
H The number of triangles formed in any regular polygon is 2 less than the number of
sides in the polygon.
J
21
The number of triangles formed in any regular polygon is half the number of sides in
the polygon.
If a conditional statement is true,
which of the following is always true?
A the inverse of the statement
22
Which of the following does not give
enough information to prove that
∆WXZ ∆YXZ?
B the contrapositive of the statement
C
the converse of the statement
D None of the above are always true.
F
G
bisects Z is the midpoint of H J
Page 9
and and the perpendicular bisector of GO ON
23
Lines that intersect to form right
angles are called ___ lines.
25
A parallel
If a and b are negative integers, then
their product is always positive. Which
is the best statement regarding the
converse of this conditional statement?
B skew
C
A The converse is false because a
positive product could also result
from 2 positive numbers.
intersecting
D perpendicular
24
B The converse is false because the
product of 2 negatives could also
be a negative.
Which of the following theorems
CANNOT be used to prove two lines
are parallel?
F
G
C
If two lines are cut by a
transversal so that a pair of
alternate exterior angles are
congruent, then the lines are
parallel.
If two lines are cut by a
transversal so that a pair of
vertical angles are congruent, then
the lines are parallel.
The converse is true because a
positive product can only result
from 2 negative numbers.
D The converse is true because the
product of 2 negatives is always
positive.
26
In the diagram below, segments RS
and RT intersect line DE at points T
and S.
H If two lines are cut by a
transversal so that a pair of
corresponding angles are
congruent, then the lines are
parallel.
J
If two lines are cut by a
transversal so that a pair of same
side interior angles are
supplementary, then the lines are
parallel.
Which of these statements is
TRUE about triangle RST?
F
Triangle RST is an equilateral
triangle.
G
Triangle RST is a scalene triangle
H Triangle RST is a right triangle.
J
Page 10
Triangle RST is an isosceles
triangle.
GO ON
27
Centuries ago people believed the
Earth was a flat plane, similar to a
Euclidean plane. Eventually, explorers
and astronomers disproved this notion.
Instead of modeling the earth with a
Euclidean plane, what geometric
system did mathematicians develop to
map their new discoveries about the
Earth’s surface?
A global geometry
B topological geometry
C
spherical geometry
D hyperbolic geometry
28
Anna is using a compass and a straight
edge to complete a geometric
construction using the following set of
instructions:
1. Draw a line segment with endpoints
A and B. 2. Fold your paper so that points A and
B exactly overlap. 3. Crease, then unfold the paper. 4. Mark the intersectionof the crease
and line segemnt AB. Labek this
intersection as point C.
What will Anna’s drawing best
illustrate when she is finished?
F
the midpoint of a line segment
G
parallel line segments
H an angle bisector
J
Page 11
congruent angles
GO ON
29
Marsha made the following construction using a straight edge and a compass. Starting with
a line segment, she opened the compass equal to the length of the segment. Using each
endpoint as the center of two different circles, she made arcs with the compass until they
intersected above the line segment. Marsha then used the straight edge to make two
additional line segments connecting the intersection of the arcs to each endpoint on the
initial line segment. Which of the following did Marsha construct?
A a perpendicular line segment
B an equilateral triangle
C
an inscribed circle inside of a triangle
D a circumscribed circle about a triangle
30
Since the surface of the Earth is
roughly a sphere instead of a plane, the
shortest distance between two points
along the surface of the Earth would
take the form of —
F
a straight line
G
an arc
H a circle
J
a ray
Page 12
BE SURE YOU HAVE RECORDED ALL OF YOUR ANSWERS
ON YOUR ANSWER DOCUMENT
STOP