Download Mathematics Course: Pre-AP Geometry Designated Grading Period

Mathematics
Course: Pre-AP Geometry
Unit 5: Congruent Triangles (cont)
Unit 6: Relationships with Triangles (begin)
TEKS
Guiding Questions/
Specificity
Designated Grading Period: 3rd
Days to teach: 12
Assessment
Vocabulary
Instructional
Strategies
Resources/
Weblinks
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the oneand two-dimensional coordinate systems to verify geometric conjectures.
G.2(B) derive and
Use the distance formula to Graph the quadrilateral with the given
Distance
-Use Pythagorean
Big Ideas Geometry
use the distance, slope, verify geometric
vertices in a coordinate plane. Then
Slope
Theorem (previous
5.8, 6.1
and midpoint formulas relationships, including
show that the quadrilateral is a
Midpoint
knowledge) to derive
to verify geometric
congruence of segments.
parallelogram.
Length
Distance Formula
relationships,
Parallel
-Relate concept of
including congruence
Use the midpoint formula
A(0,0), B(1,4), C(6,6), D(5,2)
Perpendicular
midpoint to the
of segments and
to verify geometric
Quadrilateral
concept of average
parallelism or
relationships.
Parallelogram
perpendicularity of
Rectangle
pairs of lines.
Rhombus
Square
Readiness Standard
Misconception:
 The student may substitute the x- and y-values incorrectly when using
the formulas. (ie: substitute the y value for x)
 The student may divide a value by “2” instead of takin gthe square root
when using the distance formula.
 The student may add the x-value to the y-value, instead of computing
the sum of the x-values and computing the sum of the y-values before
dividing by 2 in the midpoint formula.
 The student may incorrectly write the ratio of the slope of a line as the
ratio of horizontal change divided by the vertical change (ie. x2  x1 ).
y2  y1
2016-2017
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Mathematics
Course: Pre-AP Geometry
Unit 5: Congruent Triangles (cont)
Unit 6: Relationships with Triangles (begin)
TEKS
Guiding Questions/
Specificity
Designated Grading Period: 3rd
Days to teach: 12
Assessment
Vocabulary
Instructional
Strategies
G.(5) Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures.
G.5(A) investigate
Investigate patterns to
Jordan provided the information to
Diagonal
Connect formula for
patterns to make
make conjectures about
Equilateral polygon
sum of the interior
prove that LMN  NQP using
conjectures about
geometric relationships,
Equiangular
polygon
angles of a triangle to
the SAS Congruence Theorem. Is his
geometric
including:
Regular
polygon
the formula for sum of
information correct?
relationships,
Exterior angle
the interior angles of a
 criteria for triangle
including angles
Interior
angle
polygon
congruence
formed by parallel
Exterior
angle
 special segments of
lines cut by a
Convex
triangles.
transversal, criteria
Parallelogram
required for triangle
Quadrilateral
congruence, special
Diagonal
segments of triangles,
Segment bisector
diagonals of
Perpendicular
quadrilaterals, interior
Correct answer:
and exterior angles of
Yes; Two pairs of sides and the
polygons, and special
included angles are congruent.
segments and angles
of circles choosing
from a variety of tools.
Readiness Standard
Resources/
Weblinks
Big Ideas Geometry
5.3, 5.5, 6.3
www.khanacademy.org
Engaging Mathematics
p. 149 (58.pdf)
Engaging Mathematics
p. 183 (71.pdf)
Misconceptions:
 The student may make a conjecture based on limited investigation of
patterns.
 The student may randomly state a conjecture without investigating and
recognizing patterns.
 The student may not know how to use a construction to make a
conjecture.
 The student may not be able to perform constructions correctly.
 The student may not state a conjecture using precise geometric
vocabulary.
2016-2017
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Mathematics
Course: Pre-AP Geometry
Unit 5: Congruent Triangles (cont)
Unit 6: Relationships with Triangles (begin)
TEKS
Guiding Questions/
Specificity
G.5(C) use the
constructions of
congruent segments,
congruent angles, angle
bisectors, and
perpendicular bisectors
to make conjectures
about geometric
relationships.
Supporting Standard
Use the constructions of
angle bisectors to make
conjectures about
geometric relationships.
Designated Grading Period: 3rd
Days to teach: 12
Assessment
In the figure shown,
QP  2 x  9 and Angle bisector
QM  5x  3 . Find QN.
Use the constructions of
perpendicular bisectors
to make conjectures
about geometric
relationships.
Vocabulary
Bisect
Congruent
Instructional
Strategies
Tracing paper is
helpful when
explorations are done
by paper folding.
Resources/
Weblinks
Big Ideas Geometry
6.1, 6.2
Consider using a local
map that your students
would be familiar with.
Take a screen shot and
import it into your
dynamic geometry
software.
Correct Answer:
QN= 17
2016-2017
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Mathematics
Course: Pre-AP Geometry
Unit 5: Congruent Triangles (cont)
Unit 6: Relationships with Triangles (begin)
TEKS
Guiding Questions/
Specificity
Designated Grading Period: 3rd
Days to teach: 12
Assessment
Vocabulary
Instructional
Strategies
Resources/
Weblinks
G.(6) Proof and congruence. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as
coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart. The student is expected to:
G.6(A) verify theorems Prove equidistance
Find the measure of GH.
Angles
Use coordinate
Big Ideas Geometry
about angles formed by between the endpoints of
Endpoints
geometry to
6.1
the intersection of lines a segment and points on
Equidistance
demonstrate
and line segments,
its perpendicular bisector.
Intersection
relationships to prove
including vertical
Line
that points on the
angles, and angles
Apply these relationships
Line segment
perpendicular bisector
formed by parallel lines to solve problems.
Parallel lines
of a segment are
cut by a transversal and
Perpendicular bisector equidistant from the
prove equidistance
“Prove” by using formal
Theorem
endpoints of the
between the endpoints
proof to be shown in
Transversal
segment.
of a segment and points
Vertical angles
 Paragraph
on its perpendicular
 Flow chart
bisector and
 Two-column
Correct Answer:
apply these
formats.
relationships to solve
4.6, because GK  KJ and
problems.
HK  GJ , point H is on the
Readiness Standard
Misconceptions:
perpendicular bisector of GJ . So, by
 The student may not use logical reasoning correctly to work through
the Perpendicular Bisector Theorem,
proofs.
GH  HJ  4.6 .
 The student may not apply justification to support statements in a twocolumn proof.
2016-2017
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Mathematics
Course: Pre-AP Geometry
Unit 5: Congruent Triangles (cont)
Unit 6: Relationships with Triangles (begin)
TEKS
Guiding Questions/
Specificity
G.6(B) prove two
triangles are congruent
by applying the SideAngle-Side, AngleSide-Angle, Side-SideSide, Angle-AngleSide, and HypotenuseLeg congruence
conditions.
Readiness Standard
Prove two triangles are
congruent by applying the
 Side-Angle-Side
 Angle-Side-Angle
 Side-Side-Side
 Angle-Angle-Side
 Hypotenuse-Leg
congruence condition.
Designated Grading Period: 3rd
Days to teach: 12
Assessment
Given AC  EC , BC  DC
Prove
ABC  EDC
Correct answer:
Given:
Can you use ASA to prove RST 
TUR? If yes, what theorem(s),
postulate(s), or property(ies) did you
use besides ASA? If no, what other
information would make it possible to
prove the triangles congruent by ASA?
Vocabulary
Instructional
Strategies
Resources/
Weblinks
Corollary
Have students keep all Big Ideas Geometry
Corresponding Angles the related definitions, 5.3, 5.5, 5.6, 5.7
Corresponding
postulates and
Polygons
theorems together.
www.khanacademy.org
Corresponding Sides
Included Angle
Use facts definitions
Engaging Mathematics
Included Side
postulates theorems
Geometry
Interior
and properties to prove p.89-90 (35.pdf)
Triangle Rigidity
statements true or
SAS
false.
SSS
ASA
Analyze and produce
AAS
proofs to solve
AL
problems
Misconceptions:
 The student may think Side-Side-Angle may be a congruence condition
that proves two triangles are congruent.
Correct answer:
a) yes
b)if parallel lines then alternate interior
angles are congruent
(∠URT ≅ ∠STR, ∠SRT ≅ ∠UTR)
Reflexive property of congruence
̅̅̅̅
RT ≅ ̅̅̅̅
RT
2016-2017
Page 5
Mathematics
Course: Pre-AP Geometry
Unit 5: Congruent Triangles (cont)
Unit 6: Relationships with Triangles (begin)
TEKS
Guiding Questions/
Specificity
G.6(D) verify theorems
about the relationships in
triangles, including proof
of the Pythagorean
Theorem, the sum of
interior angles, base
angles of isosceles
triangles, midsegments,
and medians,and
apply these relationships
to solve problems.
Supporting Standard
2016-2017
Verify theorems about
the relationships in
triangles, including
medians.
Designated Grading Period: 3rd
Days to teach: 12
Assessment
Vocabulary
Point P is the centroid of LMN . The
measure of QN = 30. Find PN and QP.
Base Angle
Interior Angles
Isosceles Triangle
Median
Mid-Segment
Pythagorean Theorem
Theorem
Triangle
Centroid
Orthocenter
Apply these relationships
to solve problems.
Methods for proving
may include coordinate,
transformations,
axiomatic, and formats
such as two-column,
paragraph, or flow chart.
Instructional
Strategies
Use rules for congruent
or similar triangles to
prove relationships.
Resources/
Weblinks
Big Ideas Geometry
6.2, 6.3
Include activities to
apply these
relationships to solve
problems.
Correct Answer:
20, 10
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