Unit 4: Proofs
Geometry
8 Class Meetings – Revised June 2016
Essential Questions
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How do you show that two triangles are congruent?
Enduring Understanding with Unit Goals
EU #1: Comparing the corresponding parts of two figures can show that the figures are
congruent, but two triangles can be proven congruent without showing ALL corresponding parts
are congruent.
o Demonstrate the congruence of all corresponding parts in order to prove two figures
congruent.
o Prove two triangles are congruent using SSS, SAS, ASA, AAS, and HL.
EU #2: If two triangles are congruent, then every pair of their corresponding parts is also
congruent.
o Prove parts of triangles are congruent using CPCTC theorem.
Standards
Common Core State Standards/College and Career Readiness Anchor Standards :
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HSG.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to
prove relationships in geometric figures.
HSG.CO.D.12: Make formal geometric constructions with a variety of tools and methods.
HSG.CO.C.10: Prove theorems about triangles.
MSMHS 21st Century Learning Expectations
Competency 1: Read and write effectively for a variety of purposes.
Competency 3: Make decisions and solve problems independently and collaboratively.
Competency 5: Contribute to a positive learning environment with respect and responsibility.
Unit 4: Proofs
Geometry
8 Class Meetings
Unit Content Overview
1. Congruent Figures
● Finding and Using Congruent Parts
● Third Angle Theorem
● Proving Figures Congruent
2. Triangle Congruence by SSS and SAS
● SSS Postulate
● SAS Postulate
3. Triangle Congruence by ASA and AAS
● ASA Postulate
● AAS Theorem
4. Congruence in Right Triangles
● Hypotenuse-Leg (HL) Theorem
● Writing a Proof Using the HL Theorem
5.
Using Corresponding Parts of Congruent Triangles
● Proving Parts of Triangles Congruent
Learning Objectives
Students will be able to…
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Recognize congruent figures and their corresponding parts
Prove two triangles congruent using the SSS and SAS Postulates
Prove two triangles congruent using the ASA and the AAS Theorem
Prove that parts of two triangles are congruent using triangle congruence and
corresponding parts of congruent triangles (CPCTC)
Prove right triangles congruent using the Hypotenuse – Leg Theorem
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Unit 4: Proofs
Geometry
8 Class Meetings
Assured Learning Experiences
Differentiated Instruction / Instructional Strategies:
● Lectures with notes
● Guided notes
● Student-led instruction
● Independent problem-solving
● Collaborative problem-solving
● Buried Treasure Performance Task (practical application)
○ Rubric 3: Problem Solving
● Cross-curricular problem solving (independent and collaborative)
● Accountable Talk
● Homework
Interdisciplinary Connection:
● Language Arts - Word Problems
● Marine Science – Word Problems
Assessments
FORMATIVE ASSESSMENTS:
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Warm ups (SAT)
ABCD Cards
Whiteboards
Mid-class check-ins
Exit Slips
Student-led instruction
Homework
Buried Treasure Performance Task
o Rubric 3: Problem Solving
SUMMATIVE ASSESSMENTS:
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Quiz 1 - Congruent Triangles, SSS, SAS, ASA, AAS Theorems - EU #1
Unit 4 Test
Buried Treasure Performance Task
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Unit 4: Proofs
Geometry
8 Class Meetings
Unit Task
Unit Task Name: Buried Treasure Performance Task
Description: Students will use information learned in this unit about how comparing the corresponding
parts of two figures can show whether the figures are congruent, how two triangles can be proven to be
congruent without having to show that all corresponding parts are congruent (EU #1) and how if two
triangles are congruent, then every pair of their corresponding parts is also congruent (EU #2) in order to
discover the buried treasure, if possible, in three different scenarios. Students will be given a set of
instructions in three different scenarios and asked to use triangle congruence to prove if the treasure can be
recovered or not. Students will need to create a map for each of the scenarios and use the theorems they
learned in class to show if they are able to find the treasure. In a well-developed paragraph, along with
their maps, students will to explain the theorems they used to come to their decisions about each map.
Evaluation: Rubric 3: Problem Solving
Unit Resources
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Textbook
MSMHS School-wide Rubrics
Flipped Classroom Videos
Worksheets
Graphing Calculator
Laptops
SAT Prep Online
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