GEOMETRY
(SECONDARY)
ESSENTIAL UNIT (E04)
(Triangle Congruence)
(July 2013)
Unit Statement: This unit investigates congruence between triangles. Triangles will be
proven to be congruent with minimal information given. Theorems regarding isosceles and
equilateral triangles are introduced and can be used in proofs.
Essential Outcomes: (must be assessed for mastery)
Problem solving and higher order thinking components are essential for A level mastery.
Each outcome can contain problem solving and higher order thinking components (as
found in suggested text).
1. The Student Will describe transformations in the coordinate plane and prove
whether figures are congruent (4.1 pp 216 - 223).
2. TSW find angle measures and side lengths of triangles and classify triangles by
their angles and sides (4.2 pp.224 - 229).
3. TSW apply the theorems about the interior and exterior angles of triangles to find
their angle measures (4.3 pp. 231 - 238).
4. TSW prove triangles congruent using the definition of congruence and properties
of congruent triangles (4.4 pp. 239 - 245).
5. TSW apply SSS and SAS to solve problems involving congruent triangles. (4.5
pp. 250 - 257).
6. TSW apply ASA, AAS and HL to solve problems involving congruent triangles
(4.6 pp. 260 - 267).
7. TSW use CPCTC to solve problems involving congruent triangles (4.7 pp. 268 - 273).
8. TSW can use geometric concepts in the coordinate plane (4.8 pp. 279 – 284).
9. TSW apply properties of isosceles and equilateral triangles (4.9 pp. 285 - 291).
Introduced and Practiced Outcomes: (taught not assessed)
1. The Student Will use paper to discover the relationship between the measures of
the interior angles of a triangle (4.3 p. 230).
Key Terms and Concepts:
acute triangle
isosceles triangle
interior
exterior
included side
equiangular triangle
obtuse triangle
corresponding parts
interior angle
included angle
equilateral triangle
right triangle
legs of a triangle
exterior angle
coordinate proof
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QSI GEOMETRY SEC E04
Copyright © 1988-2013
obtuse triangles
scalene triangle
remote interior angles
congruent polygon
Suggested Assessment Tools and Strategies:
Attached Rubric or teacher generated rubric that assesses ALL essential outcomes
(TSWs).
Suggested Resources:
Holt McDougal Geometry, Chapter 4, Sections 1 - 9.
Holt McDougal Geometry, Problem Solving Workbook
Holt McDougal Geometry, Practice Worksheets
Holt McDougal Geometry, Reading Strategies
Holt McDougal Geometry, Reteach Worksheets
Holt McDougal Geometry, Challenge Worksheets
Holt McDougal Geometry, Assessment Resources
Technology Links:
Holt McDougal Geometry, Online Edition, 6-year subscription
Holt McDougal Geometry, Interactive Answers and Solutions CD-ROM
Holt McDougal Geometry, Lesson Tutorial Videos DVD-ROM
Holt McDougal Geometry, Teacher One-Stop DVD
On Core Mathematics Deluxe Eamview Grades 6-12 CD-ROM
On Core Mathematics High School Activity Generator CD-ROM
Follett Destiny WebPath Express (found on school’s automated library system)
Tenmarks www.tenmarks.com/
Khan Academy https://www.khanacademy.org/
PhET Simulations http://phet.colorado.edu/en/simulations/category/math
EVALUATION RUBRIC FOUND ON FOLLOWING PAGE………………
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QSI GEOMETRY SEC E04
Copyright © 1988-2013
UNIT EVALUATION RUBRIC


Geometry
Essential Unit 4 (E04)
To receive a ‘B’, the student must show ‘B’ level mastery on all nine TSW’s.
To receive an ‘A’, the student must show ‘A’ level mastery in at least 5 of the 9
available TSW’s and ‘B’ level mastery on all of the remaining TSW’s.
‘A’ LEVEL
TSW
‘B’ LEVEL
1- describe transformations in
the coordinate plane and
prove whether figures are
congruent.
The student is able to
relate transformations to
objects in paintings or
archeological sites.
The student can describe
transformations in the
coordinate plane and prove
whether figures are congruent.
2- find angle measures and
side lengths of triangles and
classify triangles by their
angles and sides.
The student can create and
classify triangles in a
coordinate plane.
The student is able to find angle
measures and side lengths of
triangles and classify triangles
by their angles and sides.
3- apply the theorems about
the interior and exterior
angles of triangles to find
their angle measures.
The student can modify a
diagram by drawing
auxiliary lines to find
angle measures.
The student can apply the
theorems about the interior and
exterior angles of triangles to
find their angle measures.
4- prove triangles congruent
using the definition of
congruence and properties
of congruent triangles.
The student can assess the
changes a triangle must
undergo in order to make
it congruent to another
triangle.
The student is able to prove
triangles congruent using the
definition of congruence and
properties of congruent
triangles.
5- apply SSS and SAS to
solve problems involving
congruent triangles.
The student can apply SSS
and SAS to prove that
triangles are congruent.
The student can apply SSS and
SAS to solve problems
involving congruent triangles.
6. apply ASA, AAS and HL
to solve problems involving
congruent triangles.
The student can apply
ASA, AAS and HL to
prove that triangles are
congruent.
The student can apply ASA,
AAS and HL to solve problems
involving congruent triangles.
7. use CPCTC to solve
problems involving
congruent triangles.
The student can apply
CPCTC to prove that
triangles are congruent.
The student is able to use
CPCTC to solve problems
involving congruent triangles.
8. can use geometric concepts
in the coordinate plane.
The student can prove
geometric concepts by
using coordinate proofs.
The student can use geometric
concepts in the coordinate
plane.
9. apply properties of
isosceles and equilateral
triangles.
The student can use
congruent isosceles and
equilateral triangles to
illustrate the validity of
constructions.
The student can apply
properties of isosceles and
equilateral triangles.
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QSI GEOMETRY SEC E04
Copyright © 1988-2013
Notes