Name ________________________
Period ______
Date ____________
Geometry Unit 1 Model Curriculum Assessment
1.
Write a definition for each geometric object using one or more of the
undefined notions of point, line, and distance along a line.
a. Line segment
____
b. Circle
____
c. Parallel lines
____
2.
Use two or more appropriate terms from the list below to define a
translation. Draw a diagram to illustrate your definition.
List of terms: angle, circle, parallel, perpendicular, line segment
3.
Which of the following is a correct explanation of how to rotate point A
30 counterclockwise about point X to form point A.
a.
Draw a circle with center A and radius XA. Move point X
counterclockwise around the circle to point A such that the
measure of AXA is 30.
b.
Draw a circle with center X and radius XA. Move point A
counterclockwise around the circle to point A such that the
measure of AXA is 30.
c.
Draw a circle with XA as a diameter. Move point X
counterclockwise around the circle to point A such that the
measure of AXA is 30.
d.
Draw a circle with XA as a diameter. Move point A
counterclockwise around the circle to point A such that the
measure of AXA is 30.
4.
Line segment BC will be reflected over line m to form line segment
BC. Which of the following statements must be true?
a. Line m is the perpendicular bisector of line segment BB and line
segment CC .
b. Line BC  is perpendicular to line BC.
c. Line segment BC  is parallel to line segment BC.
d. The length of line segment BB is equal to the length of line
segment CC .
5.
Point F  is the image when point F is reflected over the line x   2
and then over the line y  3. The location of F  is 3, 7 . Which of the
following is the location of point F ?
a.
 7, 1
b.
 7, 7
c.
1, 5
d.
1, 7
6.
Triangle ABC is shown in the coordinate plane below. Draw the result
of the transformation when triangle ABC is translated 6 units to the
right and then rotated 90 clockwise about the origin.
7.
For each transformation in the table below, indicate which properties
are true by placing a check mark in every appropriate box.
The image
and preimage
are congruent
Translation
Reflection
Rotation
Dilation
The image
and preimage
are similar
but not
congruent
Lengths of
segments are
preserved
Measures of
angles are
preserved
8.
Quadrilateral PQRS is shown below. Which of the following
transformations of triangle PTS could be used to show that
triangle PTS is congruent to triangle QTR ?
a. A reflection over segment QS
b. A reflection over segment PR
c. A reflection over line m
d. A reflection over line l
9.
Triangle ABC and triangle LMN are shown in the coordinate plane
below.
Part A: Explain why triangle ABC is congruent to triangle LMN using
one or more reflections, rotations, and translations.
Part B: Explain how you can use the transformations described in Part
A to prove triangle ABC is congruent to triangle LMN by any of
the criteria for triangle congruence (ASA, SAS, or SSS).
10.
Quadrilateral ABCD is shown in the coordinate plane below.
Part A: Draw an image of quadrilateral ABCD on the coordinate plane
using reflection(s), rotation(s), and/or translation(s), label the
image as EFGH, and describe the transformation(s) you used.
Part B: Write a congruence statement for quadrilateral ABCD and its
image that you drew. Explain how you know they are
congruent.
11.
In the quadrilateral below, Ð A @ Ð C and Ð B @ Ð D.
Prove that the quadrilateral is a parallelogram.
Write an informal proof.
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12.
Using the figure above and the fact that line
is parallel to segment
AC , prove that the sum of the angle measurements in a triangle is
180. Use as many or as few rows in the table as needed.
Statements
Reasons
13.
Using the figure above, prove that vertical angles are congruent. Use
as many or as few rows in the table as needed.
Statements
Reasons
14.
Use paper folding to construct the perpendicular bisector of line
segment XY shown below. Trace and label the line segment JK.
15.
Using a compass and a straight edge, construct a 60 angle in the
space below.
16.
Using a compass and a straight edge, inscribe a regular hexagon in the
circle shown below.
Geometry Unit 1 Model Curriculum Assessment Scoring Sheet
Item
Number
SLO
Number
1
1
Scoring Key / Sample Response
Answers may vary, one possible
solution:
Line Segment – a straight line that
connects two points without extending
beyond them; Circle – the set of all
points in the plane that are the same
distance from a given point; Parallel
Lines – two lines in the same plane that
are the same distance apart
Score Points
6 points total –
2 points for each part
2 points: Student gives an accurate
description using one or more of the
undefined terms.
1 point: Student gives an accurate
description but does not use one or
more of the undefined terms.
0 points: Student gives an inaccurate
description.
2
2
Answers may vary, one possible
solution:
A translation is a transformation in
which all line segments that connect an
image point with its preimage point are
parallel and congruent.
In the translation below, segments EK,
FL, and DJ are parallel and congruent.
2 points: Student gives an accurate
explanation using two or more of the
terms and a correct diagram
1 point: Student gives an accurate
description but does not use two or
more of the terms or does not include a
correct diagram
0 points: Student gives an inaccurate
description.
3
2
b
1
4
2
a
1
5
3
a
1
6
3
7
3
1
2 points: Student fills in all rows
correctly.
1 point: Student fills in 3 rows correctly.
0 points: Student fills in less than 3
rows correctly.
8
4
d
1
9
4
Answers may vary, one possible
solution:
2 points total:
Part A: If triangle ABC is rotated 180
about the origin, it would map to
triangle LMN. Therefore, triangle ABC is
congruent to triangle LMN.
1 point for each part.
Part B: Possible answer: Because the
transformations are rigid and preserve
segment lengths, AB  LM,
BC  MN, and AC  LN.
Therefore, ABC  LMN by SSS.
Possible answer – they are rigid
transformations and therefore
preserve angle measures and side
lengths (so SAS, SSS, ASA apply)
10
4
Answers may vary, one possible
solution:
Part A:
2 points: Student graphs a quadrilateral
that is congruent to ABCD, labels it
EFGH, writes a correct congruence
statement, and uses transformations to
explain the congruence.
1 point: Student graphs a quadrilateral
that is congruent to ABCD, labels it
EFGH, and writes a correct congruence
statement, but does not use rigid
transformations to explain the
congruence.
0 points: Student provides a response
that contains multiple errors.
I rotated ABCD 90 clockwise about
the origin, and then I reflected that
quadrilateral over the x-axis to get
EFGH.
Part B: ABCD  EFGH because rigid
motions preserve the lengths of line
segments and the measures of angles
so the corresponding sides and angles
are congruent.
11
5
Answers may vary, one possible
solution:
2 points: Student proves that the
quadrilateral is a parallelogram using
statements that logically follow from
one another with no gaps.
The sum of the measures of the four
angles of the quadrilateral is 360 . By
subtitution, the sum of the measures of 1 point: Student gives a proof that
either has one gap in the logic or one
two consecutive angles would be
assumption that cannot be made based
180 . These two consecutive angles
are also same-side interior angles for
opposite sides of the quadrilateral. As
a result of these same-side interior
angles being supplementary, the
opposite sides can then be said to be
parallel. Similarly, the other two
opposite sides can be shown to be
parallel; thus, the quadrilateral is a
parallelogram.
12
5
Answers may vary, one possible
solution:
on what was given.
0 points: Student does not give a logical
progression of statements to prove
that the quadrilateral is a
parallelogram.
2 points: Student lists a logical
progression of statements to prove the
sum of the measurements of the angles
is 180. Each statement has a correct
reason.
1 point: Student lists a logical
progression of statements to prove the
sum of the measurements of the angles
is 180. Some or all statements have
incorrect reasons.
0 points: Student does not list a logical
progression of statements to prove the
sum of the measurements of the angles
is 180.
13
5
Answers may vary, one possible
solution:
2 points: Student lists a logical
progression of statements to prove
that vertical angles are congruent. Each
statement has a correct reason.
1 point: Student lists a logical
progression of statements to prove
that vertical angles are congruent.
Some or all statements have incorrect
reasons.
0 points: Student does not list a logical
progression of statements to prove
that vertical angles are congruent.
14
6
1
Note: The crease through XY should
be perpendicular to XY and should
lay halfway between the points X and
Y.
15
6
16
6
1
2 points: Student inscribes a regular
hexagon (all angles have a
measurement of 120 ) in the circle.
1 point: Student inscribes a nonregular
hexagon in the circle, OR the student
constructs a regular hexagon in the
circle but not all vertices are touching
the circle.
0 points: Student constructs a figure
that does not meet the requirements
for a 2 or 1.