Geometry Unit 1
Geometry 1-2 Angles, Lines, and Reasoning Unit
Learning Goal 1: Building Blocks
Advanced
Score 5.0
In addition to score 4.0 performance, in-depth inferences and applications that goes beyond
what was taught
 Justify how many angles are needed to find all the angles in a diagram of several
intersecting lines;
 Apply complex algebraic properties to geometric concepts (systems, quadratics…)
 Use vocabulary from this learning goal to define geometric terms learned in later units
(i.e. external angle, square)
Score
In addition to score 4.0 performance, partial success at inferences and applications
4.5
that goes beyond what was taught
Proficient
Score 4.0
No major errors or omissions regarding any of the information and/or processes (simple or
complex) that was explicitly taught.
While engaged in grade-appropriate tasks, the student identifies errors and demonstrates an
understanding of lines, angles, and geometric objects by…
 Finding angle measures given algebraic expressions and properties of lines and angles;

Apply the segment addition postulate and angle addition postulate.

Apply properties of vertical angles and linear pairs.

Apply properties of complementary and supplementary angles

Apply algebraic properties to geometric concepts
Score
No major errors or omissions regarding the simpler details and/or processes and
3.5
partial knowledge of the more complex ideas and processes.
Basic
Score 3.0
No major errors or omissions regarding the simpler details and processes, but major errors or
omissions regarding the more complex ideas and processes.
The student exhibits no major errors or omissions regarding the simpler details and
processes, such as . . .

Appropriately name and sketch points, lines, angles, and planes.

Recognize and mark congruency in a diagram.

Recognize vertical angles and linear pairs (including properties).

Recognize complementary and supplementary angles (including properties)
 Recognize and recall specific terminology (See learning goal 1 vocabulary);
 Recognize the accuracy of basic solutions and information, such as . . .
o Three-dimensional objects have depth, whereas two-dimensional objects do not;
o Bisectors divide objects into two congruent parts;
o Intersecting lines and associated angles
Score
Partial knowledge of the simpler details and processes, but major errors or
2.5
omissions regarding the more complex ideas and processes.
Below Basic
Score 2.0
With help, a partial understanding of some of the simpler details and processes and some of
the more complex ideas and processes.
Score
1.5
With help, a partial understanding of some of the simpler details and processes but
not more complex ideas and processes.
Score 1.0
Even with help, no understanding or skill demonstrated.
Score 0.0
There is no evidence or demonstration of student learning.
Adapted from: Marzano (2004) Workshop materials. Centennial, CO: Marzano & Associates.
Geometry 1-2 Angles, Lines, and Reasoning Unit
Learning goal 2: Logical Reasoning
Advanced
Score 5.0
In addition to score 4.0 performance, in-depth inferences and applications that goes beyond
what was taught
 Writing a proof for geometry concepts not yet covered in class (i.e. congruent triangles,
proving a quadrilateral is a square or rectangle, etc…)
 Writing a proof from scratch using geometric concepts covered in class (i.e. bisectors,
congruent angles and segments, etc…)
Score
In addition to score 4.0 performance, partial success at inferences and
4.5
applications that goes beyond what was taught
Proficient
Score 4.0
No major errors or omissions regarding any of the information and/or processes (simple or
complex) that was explicitly taught.
While engaged in grade-appropriate tasks, the student identifies errors and demonstrates
an understanding of logical reasoning by…
 Writing the different forms of a conditional statement;
 Determining if a definition is valid using the biconditional statement;
 Justifying the reasoning for an answer when geometric concepts are involved. (i.e.
Vertical angles are congruent, bisecting means divide a figure in half, etc…)
 Completing a “fill in the blank” proof with more than half of the proof missing.
Score
No major errors or omissions regarding the simpler details and/or processes and
3.5
partial knowledge of the more complex ideas and processes.
Basic
Score 3.0
No major errors or omissions regarding the simpler details and processes, but major errors
or omissions regarding the more complex ideas and processes.
The student exhibits no major errors or omissions regarding the simpler details and
processes, such as . . .
 Identifying different forms of a conditional statement;
 Identifying the difference between a conditional statement and a biconditional
statement;
 Justifying the reasoning for an algebraic answer;
 Justifying the reasoning for a given example;
 Filling a partially completed proof or reordering statements and reasons in a logical
order (i.e. “puzzle proofs”);
Score
Partial knowledge of the simpler details and processes, but major errors or
2.5
omissions regarding the more complex ideas and processes.
Below Basic Score 2.0
With help, a partial understanding of some of the simpler details and processes and some of
the more complex ideas and processes.
Score
1.5
With help, a partial understanding of some of the simpler details and processes
but not more complex ideas and processes.
Score 1.0
Even with help, no understanding or skill demonstrated.
Score 0.0
There is no evidence or demonstration of student learning.
Adapted from: Marzano (2004) Workshop materials. Centennial, CO: Marzano & Associates.
Unit One Test – Geometry 1-2 Angles, Lines, and Reasoning Unit
Name: ___________________________
Date: _______
Learning Goal 1, Level 3 Questions
1. Sketch three points that are not collinear.
2. Choose the correct name for the given figures.
A.
B.
A
C
B
A
a
E
B
a) ∠EBC
b) ∠C
c) ∠ACE
C.
D.
P
N
R
O
T
V
C
a) ⃡𝐶𝐵𝐴
b) 𝑎
⃡
c) ⃡𝐴𝐵𝐶
d) ∠BCA
d) answers a, b, and c
e) both answers c and d e) none of the above
a) ̅̅̅̅
𝑉𝑇
a) 𝑃𝑂
̅̅̅̅̅̅
b) 𝑅𝑇𝑉
c) ̅̅̅̅
𝑉𝑅
b) 𝑁𝑂
c) ⃡𝑂𝑃
⃡
d) 𝑁𝑃
e) all of the above
̅̅̅̅
d) 𝑅𝑇
e) answers b and c
3. If 𝐴𝐵 bisects ∠𝐿𝐴𝑋 and ∠𝐿𝐴𝐵 measures 68°, find the measure of ∠𝑋𝐴𝐵.
Refer to the figure at the right to answer questions 4 – 7. Fill in the blank with the letter from the answer bank that
corresponds with the best answer.
B
______4. Identify an angle supplementary to ∠AOE
______5. Identify an angle complementary to ∠BOC
C
A
O
______6. Identify an angle adjacent to ∠AOB
E
______7. Identify an angle that forms a linear pair with ∠EOB
Use the figure above to name the specified objects for 8 and 9.
8. Name a line containing point E.
D
Answer Bank
A. ∠BOD
B. ∠EOD
C. ∠COD
D. ∠BOC
E. ∠COE
9. Name a line segment containing point A.
10. Name a ray opposite to (ray) OE.
11. Describe the method used to name any plane.
X
Mark the figure at the right to illustrate the following givens.
Q
12. ∠QAX is congruent to ∠WAZ
Y
A
13. ∠QAU is a right angle.
U
14. Point A is the midpoint of ̅̅̅̅̅
𝑄𝑊
B
Z
W
Identify the figure as two dimensional or three dimensional
15.
16.
17.
Learning Goal 1, Level 4
18. If an obtuse angle is bisected, the resulting angles are _________.
a. always acute b. never congruent
c. right angles
d. always obtuse
Give an examples or draw a picture to explain why you chose the answer you did for this question.
L
19. In the figure, 𝑀𝑂 bisects ∠𝐿𝑀𝑁.
m∠𝐿𝑀𝑂 = (13x – 31)°
m∠𝑁𝑀𝑂 = (x + 53)°
Solve for x and find m∠𝐿𝑀𝑁.
O
x = _________
m∠𝐿𝑀𝑁 = ____________
M
N
20. Let D be between E and F. Solve for x and find ED and DF. Use the space provided to sketch the figure and show
your work.
x = ______
ED = 4x + 10
DF = 2x + 20
EF = 54
ED = ______
DF = ______
21. Find the measure of angles 1,2, & 3. Justify your answers.
m ∠1 = ________________ Because: __________________
78o
1
3
2
m ∠2 = ________________ Because: __________________
m ∠3 = ________________ Because: __________________
22. A and B are complementary. Given: mA = (3x), and mB = (x + 8). Find x, m∠A, and m∠B.
x = ___________
mA = _________°
mB = _________°
Learning goal 1, Level 5
23. Using the vocabulary you learned in this unit, give a geometric definition of a square.
24. Given ∠PQR, let M be the midpoint of ̅̅̅̅
𝑃𝑅. Can you conclude that ̅̅̅̅̅
𝑄𝑀 bisects ∠PQR? If so, explain why. If not,
sketch a counterexample.
Learning goal 2, Level 3
Match the appropriate statement with its symbolic notation and description. Use “p” for the hypothesis and “q” for the
conclusion.
Symbolic Notation choices
a) ~ q  ~ p
Description Choices
h) Negate the hypothesis and keep the conclusion
b) q  p
i) Use the given hypothesis and the conclusion and the
c) ~ p  q
words “if” and “then”
d) p  q
j) Geometry teachers rock!
e) p  q
k) Negate and switch the hypothesis and the conclusion
f) ~ q  p
l) Negate both the hypothesis and the conclusion
g) ~ p  ~ q
m) Switch the hypothesis and the conclusion
n) A true conditional statement and its true converse
Statement
Symbolic Notation (a-g)
25. Conditional Statement
26. Converse
27. Inverse
28. Contrapositive
29. Biconditional
30. Identify the missing justifications.
2x + 6(x – 3) = 150
_________________________
2x + 6x – 18 = 150
_________________________
8x – 18 = 150
_________________________
8x = 168
_________________________
x = 21
_________________________
Description (h-n)
Learning goal 2, Level 4
31. Given the statement below, write the converse, inverse, and contrapositive. Then indicate if the statement is true or
false. If false, write a counterexample.
If two angles are vertical, then they are congruent.
Converse:
True False
Inverse:
True False
Contrapositive:
True False
32. Fill in each blank.
Given: W and V are congruent and supplementary.
Prove: W and V are right angles
W and V are congruent because ______________________ . Because congruent angles have the same
measure, the mW = __________. W and V are supplementary because it is given. By the definition of
____________________________________, mW + mV = 180°. Substituting mW for mV, you get
mW + mW = 180°, or 2mW = 180°. By the _____________________ property of equality, mW = 90°.
Since mW = mV, the mV = 90° by the transitive property of equality. Both angles are _______________
by the definition of right angles.
33. Is it appropriate to write the following two statements as a biconditional? If so, write the biconditional.
Hypothesis: an angle is a right angle
Conclusion: an angle measures 90°
Learning goal 2, Level 5
34.
A. Complete the following statement:
If a red marble hits a blue marble, and the blue marble hits a green marble, and the green marble hits a yellow
marble, then the ___________ marble caused the yellow marble to move.
B. Describe the reasoning that supports your answer.
35. Explain what is wrong with the following argument: Note that ∠1 and ∠3 are vertical angles, and ∠2 and ∠4 are also
vertical angles. Since ∠1 is a vertical angle and ∠2 is a vertical angle, and vertical angles are congruent, we may conclude
that ∠1 ≅ ∠2.
1
2
4
3
36. Complete the proof below.
Given: m  ABC = 100°
Prove: m  4 + m  2 = 100°
1
A
2
B
3
4
C