Geometry Units - Triangles and Congruency

Index
Algebra I Units
Algebra II Units
Language Arts
Science

Geometry Units

·	Lines & Vectors
·	Points, Lines, Planes, & Angles
·	Logic and Proof
·	Triangles and Congruency
·	Right Triangle Relationships
·	Similar Triangles
·	Polygons
·	Circles
·	3D Figures
·	Transformations

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Westmoreland County Public Schools

High School Curriculum

Geometry Units - Triangles and Congruency

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Geometry | Measurement | Technology

Geometry

Congruency/Similarity: Triangles/Proofs
The learner will be able to prove the congruence of triangles using different proof formats (G.5.b).

Bloom's	Scope	Activities
	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

Congruent/Similar: Problem Solving
The learner will be able to both represent and solve problems using properties of congruent triangles (G.5.b).

Bloom's	Scope	Activities
	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

Congruent/Similar: Figures
The learner will be able to demonstrate an understanding of congruent figures by utilizing the properties of these figures to solve problems and to prove solutions (G.5. a, b; G.8. a, b, c).

Bloom's	Scope	Activities
	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

Angles: Polygons/Problem Solving
The learner will be able to both represent and solve problems using the interior and exterior angles of triangles. (G.3, G.9).

Bloom's	Scope	Activities
	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

Triangles: Congruency/Similarity
The learner will be able to explore and recognize relationships involving congruence that may be present between triangles (G.5.a).

Bloom's	Scope	Activities
	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

Logic: Deductive Arguments
The learner will be able to incorporate definitions, postulates, theorems, and logical reasoning techniques to develop deductive arguments in paragraph form, flow chart form, or formal proofs to solve real-world scenario and class problems. (G.1.d).

Bloom's	Scope	Activities
	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

Deductive Reasoning
The learner will be able to use deductive reasoning to solve problems (G.1.d).

Bloom's	Scope	Activities
Analysis	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

Congruency: SAS/ASA
The learner will be able to determine side - angle - side (SAS), angle - side - angle (ASA), AAS, SSS, and SSA congruence in triangles using the angle sum property for triangles and the Pythagorean theorem (G.5. a, b).

Bloom's	Scope	Activities
Comprehension	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

Congruency: Applying
The learner will be able to use congruent triangles in problem solving situations (G.3; G.8.c).

Bloom's	Scope	Activities
Application	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

Proofs: Angle Measures Theorem
The learner will be able to compose formal proofs where theorems related to angle measures of triangles are applied (G.5.b).

Bloom's	Scope	Activities
Synthesis	Master	Classroom

Unit Instructional Resources

·	Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
·	Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	MIRA's, N/A, N/A, Math Office [Manipulative]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
·	Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
·	Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]

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Technology

Calculator: Approximations
The learner will be able to apply approximations suitably in computations made with calculators and identify errors occurring as a result (G.7; G.13).

Bloom's	Scope	Activities
	Master	Classroom

Unit Instructional Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]

Geometry: Congruency/Similarity
The learner will be able to use calculators to solve problems with congruent triangles (G.5.a).

Bloom's	Scope	Activities
Comprehension	Master	Classroom

Unit Instructional Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]

Unit Assessment Resources

·	Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
·	Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
·	TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
·	TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
·	Skills Connection, EdVision, 2001, Classroom - Computer [Tests]

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Measurement

Area/Per: Relationships Holding Constant
The learner will be able to analyze the relationships, either between figures with a specific perimeter and their possible area measurements, or between figures with a specific area and their possible perimeters (G.13; G.14).

Bloom's	Scope	Activities
	Master	Classroom

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