Download Chapter Four Learning Objectives Congruent Triangles

Chapter Four Learning Objectives
Congruent Triangles
What enduring understandings are desired?
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Students will understand that proving triangles congruent can be done in a variety of
different ways.
Students are able to see geometric relationships are evident in real-life situations.
Students will be able to recognize math processes in the future and be able to locate
appropriate resources and materials to assist them.
Students will be able to recognize reasoning and proof as fundamental aspects of
mathematics.
Students will be able to see relationships that exist between the angles and sides of
geometric figures can be proven.
At the conclusion of this unit the students should be able to use properties, theorems and
postulates to prove the congruency of triangles to one another
What essential questions will guide this unit and focus teaching?
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What are the properties of a triangle?
What are the different types of triangles?
How can I identify congruent triangles?
What are corresponding parts of congruent figures?
To prove triangles congruent, must you show all six corresponding sides and angles are
congruent?
What are the ways to prove triangles are congruent?
What key knowledge will students acquire as a result of this unit?
Shown Via Daily Lesson Objectives:
4.1 Classifying Triangles Objectives
 The learner will be able to classify triangles by side length
 The learner will be able to classify triangles by angle measure
 The learner will be able to use triangle classification to find angle measures and side
lengths
 The learner will be able to classify triangles and use properties of triangles to solve
problems
4.2 Angle Relationships in Triangles Objectives
 The learner will be able to find the measures of interior and exterior angles of triangles
 The learner will be able to apply theorems about the interior and exterior angles of
triangles
 The learner will understand and apply The Triangle Sum Theorem
 The learner will understand the relationship between the exterior angle of a triangle and
its two remote interior angles
4.3 Congruent Triangles Objectives
 The learner will be able to use properties of congruent triangles
 The learner will be able to identify corresponding parts of congruent figures
 The learner will be able to define congruence in triangles
 The learner will be able to create accurate congruence statements
 The learner will understand that if two angles of a triangle are congruent to two angles of
another triangle, the remaining angles will also be congruent
 The learner will be able to prove triangles congruent by using the definition of
congruence
4.4 Triangle Congruence: SSS and SAS Objectives
 The learner will understand that proving two triangles are congruent does not
necessarily require showing all six congruence statements are true
 The learner will be able to apply SAS and SSS to construct triangles and to solve
problems
 The learner will be able to prove triangles congruent by using SSS and SAS
4.5 Triangle Congruence: ASA, AAS, and HL Objectives
 The learner will be able to apply ASA, AAS, and HL to construct triangles and to solve
problems
 The learner will be able to prove triangles congruent using ASA, AAS, and HL
 The learners will know all of the different theorems and postulates that can prove
congruence, and which combinations of sides and angles do not prove congruence.
 The learner will understand that SSA does not necessarily prove triangles are congruent.
4.6 Triangle Congruence: CPCTC Objectives
 The learner will understand that if two triangles are congruent then the three pairs of
corresponding sides are congruent and the three pairs of congruent angles are
congruent.
 The learner will be able to use CPCTC to prove parts of congruent triangles are congruent
4.8 Isosceles and Equilateral Triangle Objectives
 The learner will be able to prove theorems about isosceles and equilateral triangles
 The learner will be able to apply properties of isosceles and equilateral triangles
 The learner will be able to prove that an equiangular triangle must also be equilateral
and vice versa
What key mathematical processes and practice skills will students attain
throughout the lesson?
NCTM Mathematical Practices Objectives for Congruent Triangles:
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Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Performance Processes Objectives for Congruent Triangles:
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Apply problem-solving skills (e.g., identifying irrelevant or missing information,
making conjectures, extracting mathematical meaning, recognizing and performing
multiple steps when needed, verifying results in the context of the problem) to the
solution of real-world problems
Use a variety of strategies to set up and solve increasingly complex problems
Use the language of mathematics to communicate increasingly complex ideas orally
and in writing, using symbols and notations correctly
Make mathematical connections among concepts, across disciplines, and in everyday
experiences
Use inductive reasoning to make conjectures and deductive reasoning to arrive at
valid conclusions
Read and write different types and formats of proofs including two-column, flowchart, paragraph, and indirect proofs
Understand and apply vocabulary, postulates, and theorems