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Student Name: ______________________
Teacher:
______________________ Date: ___________
District:
Miami-Dade County Public Schools
Assessment:
9_12 Mathematics Geometry Benchmark 1
Description:
Geometry Topic 3
Form:
201
1. Yuri drew triangle ABC then reflected it over line m to create triangle WXY.
Yuri concludes that the triangles are congruent. Which is a correct validation for this
conclusion?
A.
B.
C.
D.
When the triangle was reflected, the height of the resulting triangle is parallel to the
height of the original triangle.
When the triangle was reflected, the base of the resulting triangle lies on the same line
as the base of the original triangle.
When the triangle was reflected, the corresponding sides and angle measures of the
resulting triangle are the same as the original triangle.
When the triangle was reflected, the corresponding sides of the resulting triangle have
slopes that are opposite to the slopes of the original triangle.
2. Sam is studying a geometric drawing. He observes that
vertical angles and that
and
are congruent. He proves that
postulate uses Sam's information to prove that
A.
Angle-Side-Angle (ASA)
B.
Hypotenuse Leg (HL)
C.
Side-Side-Angle (SAS)
D.
Side-Side-Side (SSS)
and
are obtuse
Which
is transformed on a coordinate plane to obtain its congruent image
3.
Which
of the following statements could be true?
I.
is the translated image of
II.
is the reflected image of
III.
is the rotated image of
A.
only I
B.
only II
C.
I, II, and III
D.
only I and II
4. Figure 1 is reflected across a vertical line, translated up, and rotated counterclockwise
fewer than 90 degrees. The resulting figure is represented by Figure 2, as shown below.
Which angle MUST be congruent to
A.
B.
C.
D.
5. In the figure below,
is a reflected image of
Anne states that reflections preserve side lengths, so
and
therefore the triangles 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
6. The figure below shows
If
A.
B.
and
and
on a coordinate plane.
units, which statement is true?
The triangles are similar because dilations preserve only angle measure, so
The triangles are similar because dilations preserve only angle measure, so
C.
The triangles are congruent because they can be mapped onto each other through
reflection, so
and
units.
D.
The triangles are congruent because they can be mapped onto each other through
reflection, so
and
units.
7. What is the perimeter of the rectangle shown on the coordinate grid?
A.
12 units
B.
15 units
C.
24 units
D.
30 units
8. In triangle
theorem?
A.
B.
C.
D.
and
Which of these can be proved using the triangle sum
9. A triangle ABC and its translated image XYZ are shown below.
What relationship CANNOT be used to prove that triangle ABC is congruent to triangle
XYZ?
A.
Angle-Angle-Angle
B.
Angle-Side-Angle
C.
Side-Angle-Side
D.
Side-Side-Side
10. A rectangle on a coordinate grid has vertices at
and
The rectangle
is rotated 90° clockwise about the origin and then translated 6 units up and 2 units right.
Which graph correctly shows the transformed rectangle?
A.
B.
C.
11. Which of these would prove that triangle PQS is congruent to triangle RQT?
A. Triangle PQS is a dilation of triangle RQT, so the triangles are congruent by AAA.
B.
Triangle PQS is a dilation of triangle RQT, so the triangles are congruent by SSS.
C.
Triangle PQS is a reflection of triangle RQT, so the triangles are congruent by SSS.
D. Triangle PQS is a reflection of triangle RQT, so the triangles are congruent by AAA.
12. Which sequence of transformations will result in an image that is NOT congruent to
graphed on the coordinate grid below?
A.
a translation 4 units to the left followed by a reflection across the x-axis
B.
a reflection across the y-axis followed by a rotation 90° clockwise about the origin
C.
a dilation by a scale factor of 2 about the origin, followed by a translation 3 units down
a rotation 90° clockwise about the origin followed by a dilation by a scale factor of 1
about the origin
D.
13. Mike wants to prove that the diagonals of parallelogram JORD bisect each other. To do
that, he labels the intersection of the diagonals as point N and composes the proof
shown below.
Step
Justification
1 JORD is a parallelogram.
Given
2
Opposite sides of a parallelogram are congruent.
3
?
Definition of a parallelogram
4
and
?
?
5
6
and
Corresponding parts of congruent triangles are
congruent.
7
and
Definition of congruent line segments
8 N is the midpoint of
bisects
9
and
and
Definition of midpoint
bisects
Definition of segment bisector
The statement of step 3, and the justifications for steps 4 and 5, are missing from this
copy. Which set of statements correctly completes Mike’s proof?
A.
B.
C.
D.
14. Given the figure below, which one piece of evidence would allow the triangles to be
proven congruent?
A.
B.
C.
was reflected over line
to result in
D.
was dilated about a point on line
to result in
15. On a set of parallel lines cut by a transversal,
value of x could show that
A.
B.
C.
D.
16. Triangle
and
and
Which
are corresponding angles, and why?
Corresponding angles are congruent.
Corresponding angles are congruent.
Corresponding angles are supplementary.
Corresponding angles are supplementary.
is located in the third quadrant of a coordinate plane. If triangle
reflected across the y-axis to obtain triangle,
which statement is true?
A.
lies in quadrant II and is congruent to
B.
lies in quadrant IV and is congruent to
C.
lies in quadrant II and is not congruent to
D.
lies in quadrant IV and is not congruent to
is
17. Patricia uses the given isosceles triangle ABC to prove that the base angles of an
isosceles triangle are congruent. The statements associated with the proof are listed
below.
Which of these reasons does NOT justify any of the statements given above?
A.
CPCTC
B.
reflexive property
C.
SAS postulate of congruence
D.
definition of perpendicular lines
18. Maggie drew triangle ABC and then drew triangle DBE.
Triangle ABC is congruent to triangle DBE only if
A.
29°
B.
55°
C.
62°
D.
89°
19.
A.
B.
C.
D.
Which statement must be true?
is equal to what value?
20. Use the given triangles to answer the question.
Triangle JKL is reflected across line a to form triangle MNO. Which one of these is true?
A.
B.
C.
D.
21. The figure below shows isosceles triangle ABC, with
Which is a valid proof that shows
A.
B.
C.
D.
?
and
bisecting
22. The statements of a two-column proof are listed below.
What should the corresponding reasons be?
A.
B.
C.
D.
1. Given; 2. Definition of congruency; 3. Definition of congruency; 4. SAS theorem; 5.
CPCTC
1. Given; 2. Definition of congruency; 3. Reflexive property; 4. Hypotenuse-leg theorem;
5. CPCTC
1. Given; 2. Definition of perpendicular lines; 3. Definition of congruency; 4. SAS
theorem; 5. CPCTC
1. Given; 2. Definition of perpendicular lines; 3. Reflexive property; 4. Hypotenuse-leg
theorem; 5. CPCTC
23. In the graph below,
is transformed to obtain
To show that the triangles are congruent, triangle
could be transformed by which
movement(s) to fit exactly on triangle
a rotation of 180° clockwise about the origin followed by a dilation of 1.2 with the
center of dilation at the origin
a rotation of 90° clockwise about the origin followed by translations down 1 unit and
B.
left 10 units
a rotation of 270° clockwise about the origin followed by translations left 1 unit and up
C.
10 units
D. a reflection over the x-axis followed by a reflection over the y-axis
A.
24. In the figure below,
is rotated and reflected to obtain
If Amy knows that
which statement correctly lists additional information she would need to
prove the relationship between these triangles?
A.
Reflections and rotations preserve angle measures but not side lengths, so showing
can prove that the given triangles are similar by AA.
B.
Reflections and rotations preserve angle measures but not side lengths, so showing
can prove that the given triangles are similar by AA.
C.
Reflections and rotations preserve side lengths and angle measures, so showing
and
can prove that the given triangles are congruent by SSA.
D.
Reflections and rotations preserve side lengths and angle measures, so showing
and
can prove that the given triangles are congruent by SAS.
25. Elizabeth wants to prove the triangle angle sum theorem. Which steps could be part of
her proof?
A.
B.
C.
D.
Construct an altitude of one side, and then use corresponding parts of congruent
triangles.
Construct a line perpendicular to two sides of the triangle, and then use the linear pair
postulate.
Construct a line passing through a vertex and parallel to the base of the triangle, and
then use alternate interior angles.
Construct a line passing through two sides of the triangle and parallel to the base of
the triangle, and then use corresponding angles.