Unit 2A- Geometry TEST
Math II
Name: ___________________
Please show ANY and ALL work. Problems with no work may be counted wrong.
1. A set of regular polygons contains a quadrilateral, a hexagon, an octagon, and a nonagon. These polygons are
rotated about their centers by an angle x such that the quadrilateral and the octagon are carried onto themselves but
the hexagon and the nonagon are not. What could be the angle of rotation, x?
A. 45°
B. 90°
C. 120°
2. Rectangle ABCD is shown on the coordinate grid below.
Which sequence of reflections will map rectangle ABCD onto itself?
A. a reflection over the x-axis followed by a reflection over the y-axis
B. a reflection over the x-axis followed by another reflection over the x-axis
C. a reflection over the line
followed by a reflection over the line
D. a reflection over the line
followed by a reflection over the line
3. Which of these statements is NOT correct?
A. a composition of reflections across two intersecting lines is equivalent to a rotation.
B. a composition of reflections across three parallel lines is equivalent to one reflection.
C. a composition of reflections across two parallel lines is equivalent to a translation.
D. a composition of reflections across two intersecting lines is equivalent to a translation.
D. 180°
4. The figure below shows line segments a and b passing through a regular pentagon.
Which statement describes a series of transformations that will result in a pentagon that is mapped onto the
one shown?
A. rotating the pentagon 72° clockwise about its center and then reflecting it across segment a
B. rotating the pentagon 72° clockwise about its center and then reflecting it across segment b
C. rotating the pentagon 90° clockwise about its center and then reflecting it across segment a
D. rotating the pentagon 90° clockwise about its center and then reflecting it across segment b
5. What is a definition of a reflection of a point P across the x-axis to the point P’?
A.
B.
C.
D.
6. If
A.
which of the following statements must be true?
B.
C.
D.
7. Which statement must be true about the triangle below?
P
A. PQ + QS = PR + RT
B. PQR = PST
C. ST = 2 x QR
Q
R
D. < S = < T
S
T
8. If
is rotated 90 degrees clockwise about the origin and then translated 1 unit up and 2 units to the left, what
are the endpoints of the resulting image?
A.
B.
C.
D.
9. In the figure below,
is a reflected image of
Anne states that reflections preserve side lengths, so
are congruent. Tim states that reflections preserve angle measures, so
therefore the triangles are congruent.
Who is correct?
A. neither Anne nor Tim
B. both Anne and Tim
C. only Anne
D. only Tim
and
therefore the triangles
and
10. Alyssa has written the following proof.
Which of the following would correctly complete Statement 6?
A. SSS
B. SAS
C. ASA
D. AAS
C. ASA
D. AAS
11. Javier is writing the following proof:
Which of the following is the reason for Statement 5?
A. SSS
B. SAS
12. On a set of parallel lines cut by a transversal,
x could show that
and
and
Which value of
are corresponding angles, and why?
A.
Corresponding angles are congruent.
B.
Corresponding angles are congruent.
C.
Corresponding angles are supplementary.
D.
Corresponding angles are supplementary.
13. Triangle ABC with right angle BDC is shown below.
Which additional fact is needed to prove
A.
by Side-Angle-Side (SAS)?
B.
C.
D.
14. A proof of the base angle theorem is shown.
Which statements correctly complete the proof?
A.
B.
C.
D.
15. Given Point A
and Point B
on directed line segment AB, what is the y-coordinate of Point F
that partitions AB in the ratio of
A.
B.
C.
D.
16. A parallelogram has vertices (5, 0), (3, –3), (–4, –3), and (–2, 0). The diagonals of the parallelogram intersect at
their midpoints. What are the coordinates of the intersection of the diagonals?
A. (–0.5, –3)
17. On a coordinate grid,
B. (0.5, –1.5)
C. (1.5, 0)
has the endpoints
D. (4, –1.5)
What is the location of a point R on
that is two-fifths of the way from P to Q?
A.
B.
C.
D.
18. The coordinates of the midpoint of a line segment are (9, –13). The coordinates of an endpoint of the segment
are (–4, 5). What are the coordinates of the other endpoint?
A.
B.
C.
D.
19. Saul creates a piece of art. He begins with the figure shown, where
and
Saul draws a line located below and parallel to
at D. The measure of
that intersects
at C and
What is the measure of
A.
B.
C.
D.
20. A city map is placed on a coordinate grid. The post office is located at the point P(5, 35), the library is located at
the point L (15, 10), and the fire station is located at the point F (9, 25). What is the ratio of the length of PF to the
length of LF ?
A. 2 : 3
B. 3 : 2
C. 2 : 5
D. 3 : 5