Mathematics
Course: Geometry
Chapters: 1, 2, 3
Guiding Questions/
Specificity
Assessment
Designated Six Weeks: 1st
Days to teach: 29
Vocabulary
Instructional
Strategies
Resources/
Web-links
G.4 Geometric Structure: The student uses a variety of representations to describe geometric relationships and solve problems. Ever class day, every
unit throughout the course.
G.3 Geometric structure. The student applies logical reasoning to justify and prove mathematical statements. The student is expected to:
A town wants to fence in a Conjecture
G.3(D) use inductive
Draw conclusions from
Holt Geometry
Link to ELPS Instructional
rectangular section of a
number or picture
Counterexample
reasoning to formulate
2.1
Strategies:
park. The table shows five
patterns, specific
Formulate
a conjecture
http://ritter.tea.state.tx.us/rule
possible plans for the
Inductive Reasoning
Laying the
s/tac/chapter074/ch074a.html
Supporting Standard examples, or events
dimensions of this fenced
Foundations
2C,
1E
section. The changes in
Draw conclusions by
the width and the length of
using inductive reasoning
Utilize Whale story to
College Readiness
these plans follow a
to form conjectures
identify patterns.
Standard:
pattern.
http://www.thecb.state.tx.us/
collegereadiness/crs.pdf
Communication A.3.a
If six additional plans are
added to the table and
follow the same pattern,
which conclusion is not
correct?
A. The area of one of the
additional plans exceeds
624 square feet.
B. The area of one of the
additional plans is less
than 544 square feet.
C. The area in Plan 6 is
the same as the area in
Plan 5.
D. The area in Plan 7 is
less than the area In Plan
6.
Correct answer: A
Utilize inductive and
deductive reasoning in real
life situations
Released EOC 2013
Q#49
7/3/2014
Page 1
Mathematics
7/3/2014
Page 2
Mathematics
Course: Geometry
Chapters: 1, 2, 3
Guiding Questions/
Specificity
G.3(E) use deductive
reasoning to prove a
statement
Supporting Standard
College Readiness
Standard:
http://www.thecb.state.tx.us/
collegereadiness/crs.pdf
Communication A.3.a
Draw a conclusion from
given information.
Determine if a conjecture
is valid by Law of
Detachment and Law of
Syllogism.
Assessment
The two conditional
statements below are
true.
If 3 and 4 form a
linear pair, then they
are supplementary. If
3 and 4 are
supplementary, then
3 + 4 = 180°.
Based on these
conditional statements,
which statement must
also be true?
F. If 3 and 4 form
a linear pair, then 3+
4 = 180°.
G. If 3 and 4
form a linear pair, then
3 =90°,and 4=
90°.
H. If 3+ 4 =
180°, then z3 and Z4
form a linear pair.
J If Z3 and Z4 are
supplementary, then 
3 and 4 form a linear
pair.
Designated Six Weeks: 1st
Days to teach: 29
Vocabulary
Instructional
Strategies
Deductive reasoning
Link to ELPS Instructional
Strategies:
http://ritter.tea.state.tx.us/rule
s/tac/chapter074/ch074a.html
4C, 5B
Resources/
Web-links
Holt Geometry
2.3
2.5
Laying the
Foundations
Use facts definitions
postulates theorems and
properties to prove
statements true or false.
Analyze and produce proofs
to solve problems
Correct answer: F
Released EOC 2013
Q#16
7/3/2014
Page 3
Mathematics
Course: Geometry
Chapters: 1, 2, 3
Guiding Questions/
Specificity
G.3(A) determine the
validity of a
conditional statement,
its converse, inverse,
and contra-positive
Supporting Standard
Make, interpret, and/or
understand statements
such as “If p, then q” as
applied to attributes of
geometric drawings,
figures, etc.
College Readiness
Standard:
Develop conjectures in
the form of a conditional
statement
http://www.thecb.state.tx.us/
collegereadiness/crs.pdf
Geometric D.1.d
Communication A.3.b
Use counter-examples to
prove why statements
are false
Use inductive or
deductive reasoning to
prove statements true
Assessment
The following
conditional statement is
true.
If a quadrilateral is a
square, then it has four
congruent sides.
Which statement must
also be true?
A. If a quadrilateral has
four congruent sides,
then it is a square.
B. If a quadrilateral
does not have four
congruent sides, then it
is not a square.
C. If a quadrilateral is
not a square, then it
does not have four
congruent sides.
D. If a quadrilateral
does not have four
congruent sides, then it
is a square.
Designated Six Weeks: 1st
Days to teach: 29
Vocabulary
Instructional
Strategies
Conclusion
Conditional Statement
Contra-positive
Converse
Hypothesis
Inverse
Negation
Truth value
Link to ELPS Instructional
Strategies:
http://ritter.tea.state.tx.us/rule
s/tac/chapter074/ch074a.html
5B
Resources/
Web-links
Holt Geometry
2.2
Laying the
Foundations
Write conditional statements,
converse, inverse and contrapositive.
Use discussions and
brainstorming to determine
the validity of each statement
and provide a
counterexample if false
Correct answer: B
Released EOC 2013
Q#27
7/3/2014
Page 4
Mathematics
Course: Geometry
Chapters: 1, 2, 3
Guiding Questions/
Specificity
G.3(B) construct and
justify statements
about geometric
figures and their
properties
Supporting Standard
College Readiness
Standard:
http://www.thecb.state.tx.us/
collegereadiness/crs.pdf
Geometric D.1.d
Develop conjectures in
the form of a conditional
statement
Use counter-examples to
prove why statements
are false
Use inductive or
deductive reasoning to
prove statements true
Assessment
For triangles ABC and
DEF, A D and .
Based on this
information, which
statement is a
reasonable conclusion?
F. C D because
they are corresponding
angles of congruent
triangles.
G. CA FD because
they are corresponding
parts of congruent
triangles.
H. C F because
they are corresponding
angles of similar
triangles.
Designated Six Weeks: 1st
Days to teach: 29
Vocabulary
Instructional
Strategies
Conclusion
Conditional Statement
Contra-positive
Converse
Hypothesis
Inverse
Logically Equivalent
Statements
Negation
Truth value
Link to ELPS Instructional
Strategies:
http://ritter.tea.state.tx.us/rule
s/tac/chapter074/ch074a.html
5B
Resources/
Web-links
Holt Geometry
1.1, 1.2, 1.3
2.2, 2.4, 2.5, 2.6
Laying the
Foundations
Write conditional statements,
converse, inverse and contrapositive.
Use discussions and
brainstorming to determine
the validity of each statement
and provide a
counterexample if false
J. AB DE because
they are corresponding
parts of similar
triangles.
Correct answer: H
Released EOC 2013
Q#8
7/3/2014
Page 5
Mathematics
Course: Geometry
Chapters: 1, 2, 3
Guiding Questions/
Specificity
G.3(C) use logical
reasoning to prove
statements are true and
find counter examples
to disprove statements
that are false
Readiness Standard
College Readiness
Standard:
http://www.thecb.state.tx.us/
collegereadiness/crs.pdf
Geometric D.1.b, c
Make, interpret, and/or
understand statements
such as “If p, then q” as
applied to attributes of
geometric drawings,
figures, etc.
Develop conjectures in
the form of a conditional
statement
Use counter-examples to
prove why statements
are false
Use inductive or
deductive reasoning to
prove statements true
Assessment
A conditional statement
is given below.
If two interior angles
of a triangle are acute,
then the third interior
angle must be obtuse.
Which of the following
best describes this
statement?
A. This statement is
true because all obtuse
triangles have two acute
interior angles.
B. This statement is
false because the third
interior angle must also
be acute.
C. This statement is
true because a triangle
can have at most one
interior obtuse angle.
D. This statement is
false because the third
interior angle can be
acute, right, or obtuse.
Correct answer: D
Designated Six Weeks: 1st
Days to teach: 29
Vocabulary
Instructional
Strategies
Conclusion
Conditional Statement
Contra-positive
Converse
Hypothesis
Inverse
Logically Equivalent
Statements
Negation
Truth value
Link to ELPS Instructional
Strategies:
http://ritter.tea.state.tx.us/rule
s/tac/chapter074/ch074a.html
5B
Resources/
Web-links
Holt Geometry
2.2, 2.4, 2.5
3.2, 3.3
Laying the
Foundations
Write conditional statements,
converse, inverse and contrapositive.
Use discussions and
brainstorming to determine
the validity of each statement
and provide a
counterexample if false
Released EOC 2013
Q#11
7/3/2014
Page 6
Mathematics
Course: Geometry
Chapters: 1, 2, 3
Guiding Questions/
Specificity
Assessment
Designated Six Weeks: 1st
Days to teach: 29
Vocabulary
Instructional
Strategies
Resources/
Web-links
G.7 Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of
representing geometric figures and uses them accordingly. The student is expected to:
G.7(A) use one- and
Develop verbal
Coplanar
Holt Geometry
Link to ELPS Instructional
PQ is shown on the
1.1
two-dimensional
descriptions to define
Line
Strategies:
coordinate grid below.
coordinate systems to
geometric terms
Opposite Rays
http://ritter.tea.state.tx.us/rule 1.2
represent points, lines,
throughout the curriculum The coordinates of P
Plane
s/tac/chapter074/ch074a.html
and Q are integers.
Laying the
rays, line segments,
Point
4F, 3F, 1C, 4C
Foundations
Use number line and
and figures
Ray
Develop verbal descriptions
Segment
Supporting Standard coordinate plane to
to define geometric terms
represent points, lines,
Undefined Term
throughout the curriculum
rays, line segments and
geometric figures.
College Readiness
Use manipulatives and
Standard:
technology to draw
Geometric C.1.a
conclusions and discover
relationships about geometric
Point (x, y) lies on the
shapes and their properties.
perpendicular bisector
of PQ . What is the
value of x?
Correct answer: -2.5
Released EOC 2013
Q#10
7/3/2014
Use Patty paper to develop
vocabulary. Use spreadsheet
to define vocabulary terms
and represent pictorial and
symbolic representations.
Page 7
Mathematics
7/3/2014
Page 8
Mathematics
Course: Geometry
Chapters: 1, 2, 3
Guiding Questions/
Specificity
Assessment
Designated Six Weeks: 1st
Days to teach: 29
Vocabulary
Instructional
Strategies
Resources/
Web-links
G.1A Geometric structure. The student understands the structure of, and relationships within, an axiomatic system. The student is expected to:
G.1(A) develop an
Develop verbal
How are angles 1 and 8
Alternate Exterior
Holt Geometry
Link to ELPS Instructional
1.4, 1.6, 3.4
awareness of the
descriptions to define
related?
Angles
Strategies:
structure of a math
geometric terms
Alternate Interior
http://ritter.tea.state.tx.us/rule
Laying the
system, connecting
throughout the curriculum
Angles
s/tac/chapter074/ch074a.html
Foundations
definitions, postulates,
Coplanar
4F, 3F, 1C, 4C
logical reasoning, and
Use number line and
Corresponding Angles
Develop verbal descriptions
theorems
coordinate plane to
Diagonal
to define geometric terms
represent points, lines,
Parallel
Lines
College Readiness
A. Same side interior
throughout the curriculum
rays, line segments and
Perpendicular
Lines
Standard:
B. Alternate exterior
geometric
figures.
Same-Side
Interior
Geometric D.2.a
C. Alternate interior
Use manipulatives and
Angles
D. Corresponding
G.1(B) recognize the
technology to draw
Segment
historical development
conclusions and discover
Skew
Lines
Answer: B
of geometric systems
relationships about geometric
Transversal
Supporting Standard
shapes and their properties.
G.1(C) compare and
contrast the structures
and implications of
Euclidean and nonEuclidean geometries
Supporting Standard
G.9 Congruence & the Geometry of size. The student analyzes properties & describes relationships in geometric figures.
Find m angle 1.
A) Formulate & test
Prove lines are parallel
Link to ELPS Instructional
conjectures about the
given angle information.
Strategies:
http://ritter.tea.state.tx.us/rules/ta
properties of parallel &
c/chapter074/ch074a.html 2B, 3I
perpendicular lines
Prove and apply theorems
Use angle legs and/or tape on
based on exploration & about perpendicular lines.
the ground to demonstrate
concrete models
knowledge of angle pairs
formed by parallel lines cut
Answer: 155°
by a transversal.
7/3/2014
Holt Geometry:
3.1, 3.2, 3.3, 3.4
Discovering
Geometry
Geometry to Go
Khan Academy
Page 9