Congruence Logic Teacher Guide Rigid Motion Lab
Teacher Facilitation Guide | Tier 2 Intervention
Standard
CO HS.G-CO.B.7
Learning Objective
Students will verify triangle congruence by identifying a sequence of rigid motions that maps one triangle onto another, establishing that all corresponding pairs of sides and angles are congruent.
Tier 2 Scaffolds
Visual Mapping: Use of color-coded vertices to track points during transformations.Sentence Frames: Provided for both oral and written justifications.Gestural Support: Use hand motions for "Slide" (translation), "Flip" (reflection), and "Turn" (rotation).
Materials Needed
Rigid Motion Lab Slides
Congruence Detective Worksheet
Patty Paper or Transparencies
Colored Pencils (3 colors)
Instructional Routine
1
The Hook: "The Identical Twin Test" (5 mins)
Show two triangles on the slide. Ask: "If I cut this triangle out, can I lay it perfectly over the other one?" Define Congruence as a "perfect match" created through rigid motions.
2
I Do: Modeling the Mapping (10 mins)
Model using patty paper to Translate , Reflect , and Rotate a triangle to match its image. Key Phrase: "If the triangles are congruent, there MUST be a sequence of rigid motions that maps one to the other."
3
We Do: Guided Discovery (15 mins)
Students use the Congruence Detective Worksheet . Guide them to color-code corresponding vertices (e.g., Vertex A and Vertex D are both red). Use sentence frames: "First, I ______ Triangle 1 over the line..."
4
You Do: Independent Check (10 mins)
Students attempt the final scenario on the worksheet. Circulate and check for proper use of notation (e.g., segment AB $\cong$ segment DE).
High School Geometry Intervention | Congruence Unit | Lab #07
Instructional Support Details
Targeted Sentence Frames
Describing Motions
"To map $\triangle ABC$ onto $\triangle DEF$, I need to first __________ it 5 units right, then __________ it over the y-axis."
Verifying Congruence
"Since $\triangle ABC$ maps exactly onto $\triangle DEF$ using rigid motions, the triangles are __________ because all corresponding parts are __________."
Common Misconceptions
Confusing Orientation:
Students may think triangles aren't congruent because they are "facing the wrong way." Remind them that rotations and reflections change orientation but preserve congruence .
Mislabeling Vertices:
Students often map $A$ to $D$ based on position rather than correspondence. Use the "pathway" strategy—trace the motion to see where each point lands.
Progress Monitoring Look-Fors
Skill Evidence of Mastery Identify Motion Correctly names translation, reflection, or rotation required for a specific map. Map Vertices Points out that $A \to D$, $B \to E$, etc., by physically moving patty paper. Verify Congruence Uses the term "congruent" specifically because the triangles match perfectly after transformations.
Rigid Motion Lab Slides Geometry Lab
Rigid Motion Quest
Verifying Congruent Triangles
The Big Question
A B C
$\triangle ABC$
???
D E F
$\triangle DEF$
"Are these two triangles exactly the same size and shape?"
Rigid Motion Toolbox
Translate
Slide the shape left, right, up, or down.
Reflect
Flip the shape over a mirror line.
Rotate
Turn the shape around a fixed point.
Rigid motions NEVER change the size or shape!
The Congruence Rule
DEFINITION
Two shapes are congruent if there is a sequence of rigid motions that maps one shape perfectly onto the other.
Same Side Lengths
Same Angle Measures
The Match Test
Watch as we map $\triangle ABC$ to $\triangle DEF$:
1
Slide (Translate) to align vertex $A$ with $D$.
2
Turn (Rotate) until side $AB$ lands on $DE$.
3
Flip (Reflect) if necessary to match the final points.
PERFECT MATCH!
Detective Challenge
In your small group...
Use Patty Paper to trace $\triangle ABC$.
Physically Move the paper to map it.
Complete the Sentence Frames on your page.
Need Help?
Ask for a "Coordinate Hint" if you're stuck on the translation!
Congruence Detective Worksheet Congruence Detective
Activity: Mapping with Rigid Motions
Name:
Date:
WORD BANK:
Translation (Slide) Reflection (Flip) Rotation (Turn) Congruent
1
Case Study #1: The Basic Match
A B C D E F
Mission: Trace $\triangle ABC$ on patty paper and map it to $\triangle DEF$.
Step 1: Identify the Motion
To map $\triangle ABC$ onto $\triangle DEF$, I used a ____________________. I moved the triangle ________ units to the right and ________ units up.
Step 2: Correspondences
Vertex A matches Vertex ______
Side AB matches Side ______
Vertex B matches Vertex ______
Side BC matches Side ______
Vertex C matches Vertex ______
Side CA matches Side ______
2
Case Study #2: The Hidden Orientation
Look at the triangles below. Use your patty paper to find the sequence of motions needed to match them.
Triangle 1 Triangle 2
First, I ____________________ the triangle across the vertical line.
Then, I ____________________ the triangle ________ units to the right.
Are these triangles congruent? Why?
Rigid Motion Lab | Progress Check 1.1
3
Your Turn: Design a Sequence
Challenge: Map $\triangle XYZ$ to $\triangle PQR$.
Diagram Area
Plan your motions:
_______________________________
_______________________________
_______________________________
Final Justification:
Use the sentence frame below to finish your report.
"I know $\triangle XYZ$ is ______________________ to $\triangle PQR$ because I found a sequence of ________________ ________________ that maps one onto the other. This proves that all corresponding sides and angles are ______________________."
Self-Check
I can identify translations, reflections, and rotations.
I can match corresponding parts after a motion.
I can explain why rigid motions prove congruence.
Success Check Exit Ticket Evidence
Exit Ticket: Lab Check-Out
Name:
Score:
1. Use the diagram to identify the rigid motion needed to map $\triangle ABC$ to $\triangle DEF$.
A B C D E F
The rigid motion is a ____________________________.
2. Match the corresponding side lengths:
Side AB matches Side ______
Side BC matches Side ______
3. Explain your conclusion:
"Because these triangles map onto each other through rigid motions, I know they are __________________________. This means that all of their corresponding parts are __________________________."
Unit: Congruence (CO HS.G-CO.B.7)
Success Check
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