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Math V4 · Course chapter

Chapter 4: Transformations, Similarity, Pythagorean Geometry, and Volume

Geometry

Essential question: How can transformations and geometric relationships explain shape, distance, similarity, and measurement?

Where this lesson fits

Lesson 6 of 12. Each lesson builds on earlier chapter representations and ideas rather than resetting the topic.

Chapter destination

Build and defend a multi-representation model using transformations, similarity, pythagorean geometry, and volume, including interpretation, verification, and error analysis.

Learning objectives

What you should be able to do

Represent and solve understand similarity through transformations problems using precise mathematical notation, multiple representations, and justified reasoning.
Interpret and verify understand similarity through transformations results in context, including units, constraints, and reasonableness.

Prerequisite check

Make sure the foundation is ready.

Can you solve and explain prerequisite MAT-08-GEO-004 without relying on a memorized keyword?

Grade 8 uses this prerequisite as active knowledge in a more formal representation.

Learn

Build the idea from meaning, not memorization.

Chapter 4: Transformations, Similarity, Pythagorean Geometry, and Volume

Geometry. Lesson 6 of 12 extends earlier chapter reasoning.

Connection to the course

Use earlier Grade 8 chapters, Grade 7 prerequisite knowledge as active knowledge. Connect today's representation to at least one earlier representation and explain the relationship.

Meaning and structure

Understand Similarity Through Transformations belongs to geometry. Identify the governing property or relationship before choosing a procedure.

Multiple representations

Represent understand similarity through transformations numerically and symbolically, then connect it to the Grade 8 Math Box. Tables, graphs, equations, coordinate models, diagrams, and verbal descriptions must agree.

Verification and interpretation

Check with substitution, an inverse operation, an equivalent representation, geometric invariants, estimation, or context. State whether the result is exact or approximate and preserve relevant units and constraints.

Math Box · Interactive lesson

Touch the math. Change it. See what stays true.

Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.

Transformation Lab

x2y3

(2, 3) → (4, 2)

Try these actions

Model understand similarity through transformations in the Math Box.
Change one input and predict which quantities or invariants should change.
Explain what the visual, equation, and numerical result say about the same relationship.

Worked examples

Twenty different ways to see the concept work.

Case 1: a figure is dilated by 2 then rotated. Similar?

yes

Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 2: a figure is dilated by 3 then rotated. Similar?

yes

A representation makes the mathematical structure visible before calculation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Explain why the method works, not only what steps to perform: Case 3: a figure is dilated by 4 then rotated. Similar?

yes

Justification connects each step to a definition, property, or relationship. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 4: a figure is dilated by 5 then rotated. Similar?

yes

An estimate provides an independent reasonableness check. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Verify the result with substitution, an inverse operation, or a second representation: Case 5: a figure is dilated by 6 then rotated. Similar?

yes

Independent verification should support the result without merely repeating the same procedure. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Interpret the result in context, including units, direction, rate, or geometric meaning: Case 6: a figure is dilated by 2 then rotated. Similar?

yes

Interpretation connects a computed value to the mathematical situation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 7: a figure is dilated by 3 then rotated. Similar?

Rigid transformations preserve size; dilations generally do not. Correct solution: yes

Error analysis identifies the broken idea and replaces it with valid reasoning. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Compare two related cases. Explain what changes and what remains mathematically consistent. Case A: Case 8: a figure is dilated by 4 then rotated. Similar? Case B: Case 19: a figure is dilated by 5 then rotated. Similar?

Case A: yes Case B: yes

Comparison should address structure and representation, not only numerical answers. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Case 9: a figure is dilated by 5 then rotated. Similar?

yes

Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 10: a figure is dilated by 6 then rotated. Similar?

yes

A representation makes the mathematical structure visible before calculation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Explain why the method works, not only what steps to perform: Case 11: a figure is dilated by 2 then rotated. Similar?

yes

Justification connects each step to a definition, property, or relationship. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 12: a figure is dilated by 3 then rotated. Similar?

yes

An estimate provides an independent reasonableness check. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Verify the result with substitution, an inverse operation, or a second representation: Case 13: a figure is dilated by 4 then rotated. Similar?

yes

Independent verification should support the result without merely repeating the same procedure. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Interpret the result in context, including units, direction, rate, or geometric meaning: Case 14: a figure is dilated by 5 then rotated. Similar?

yes

Interpretation connects a computed value to the mathematical situation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 15: a figure is dilated by 6 then rotated. Similar?

Rigid transformations preserve size; dilations generally do not. Correct solution: yes

Error analysis identifies the broken idea and replaces it with valid reasoning. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Compare two related cases. Explain what changes and what remains mathematically consistent. Case A: Case 16: a figure is dilated by 2 then rotated. Similar? Case B: Case 27: a figure is dilated by 3 then rotated. Similar?

Case A: yes Case B: yes

Comparison should address structure and representation, not only numerical answers. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Case 17: a figure is dilated by 3 then rotated. Similar?

yes

Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 18: a figure is dilated by 4 then rotated. Similar?

yes

A representation makes the mathematical structure visible before calculation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Explain why the method works, not only what steps to perform: Case 19: a figure is dilated by 5 then rotated. Similar?

yes

Justification connects each step to a definition, property, or relationship. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 20: a figure is dilated by 6 then rotated. Similar?

yes

An estimate provides an independent reasonableness check. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Practice

Guided practice with hints

01Verify the result with substitution, an inverse operation, or a second representation: Case 21: a figure is dilated by 2 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: yes

02Interpret the result in context, including units, direction, rate, or geometric meaning: Case 22: a figure is dilated by 3 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: yes

03Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 23: a figure is dilated by 4 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: Rigid transformations preserve size; dilations generally do not. Correct solution: yes

04Compare two related cases. Explain what changes and what remains mathematically consistent. Case A: Case 24: a figure is dilated by 5 then rotated. Similar? Case B: Case 35: a figure is dilated by 6 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: Case A: yes Case B: yes

05Case 25: a figure is dilated by 6 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: yes

06Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 26: a figure is dilated by 2 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: yes

Practice

Independent practice

01Explain why the method works, not only what steps to perform: Case 27: a figure is dilated by 3 then rotated. Similar?

Answer: yes

02Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 28: a figure is dilated by 4 then rotated. Similar?

Answer: yes

03Verify the result with substitution, an inverse operation, or a second representation: Case 29: a figure is dilated by 5 then rotated. Similar?

Answer: yes

04Interpret the result in context, including units, direction, rate, or geometric meaning: Case 30: a figure is dilated by 6 then rotated. Similar?

Answer: yes

05Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 31: a figure is dilated by 2 then rotated. Similar?

Answer: Rigid transformations preserve size; dilations generally do not. Correct solution: yes

06Compare two related cases. Explain what changes and what remains mathematically consistent. Case A: Case 32: a figure is dilated by 3 then rotated. Similar? Case B: Case 43: a figure is dilated by 4 then rotated. Similar?

Answer: Case A: yes Case B: yes

07Case 33: a figure is dilated by 4 then rotated. Similar?

Answer: yes

08Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 34: a figure is dilated by 5 then rotated. Similar?

Answer: yes

Common mistakes

Learn to catch the error, not just the answer.

Assuming every transformation preserves size.

Rigid transformations preserve size; dilations generally do not.

Using the Pythagorean theorem on a non-right triangle.

a²+b²=c² applies to right triangles.

Applications & challenge

Use the idea beyond a single exercise.

Applications

Use transformations in design and coordinate geometry and Pythagorean reasoning for distance.
Model capacities of cylindrical, conical, and spherical objects.

Challenge problems

Explain why the method works, not only what steps to perform: Case 35: a figure is dilated by 6 then rotated. Similar?

yes

Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 36: a figure is dilated by 2 then rotated. Similar?

yes

Verify the result with substitution, an inverse operation, or a second representation: Case 37: a figure is dilated by 3 then rotated. Similar?

yes

Interpret the result in context, including units, direction, rate, or geometric meaning: Case 38: a figure is dilated by 4 then rotated. Similar?

yes

Flashcards

Retrieve it from memory.

Flashcards

Card 1 of 4

Game mode

Grade 8 Algebra & Modeling Sprint

Solve understand similarity through transformations problems and justify each result with a valid verification method.

Round 1 · Score 0Explain why the method works, not only what steps to perform: Case 35: a figure is dilated by 6 then rotated. Similar?

1 point for an accurate result and 1 point for a correct explanation or verification.

Practice

Mastery check

01Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 39: a figure is dilated by 5 then rotated. Similar?

Answer: Rigid transformations preserve size; dilations generally do not. Correct solution: yes

02Compare two related cases. Explain what changes and what remains mathematically consistent. Case A: Case 40: a figure is dilated by 6 then rotated. Similar? Case B: Case 51: a figure is dilated by 2 then rotated. Similar?

Answer: Case A: yes Case B: yes

03Case 41: a figure is dilated by 2 then rotated. Similar?

Answer: yes

04Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 42: a figure is dilated by 3 then rotated. Similar?

Answer: yes

05Explain why the method works, not only what steps to perform: Case 43: a figure is dilated by 4 then rotated. Similar?

Answer: yes

06Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 44: a figure is dilated by 5 then rotated. Similar?

Answer: yes

07Verify the result with substitution, an inverse operation, or a second representation: Case 45: a figure is dilated by 6 then rotated. Similar?

Answer: yes

08Interpret the result in context, including units, direction, rate, or geometric meaning: Case 46: a figure is dilated by 2 then rotated. Similar?

Answer: yes

Terminology

Words to know

transformation: A rule mapping a figure to an image.
congruent: Having the same size and shape.
similar: Having equal corresponding angles and proportional corresponding lengths.
Pythagorean theorem: For a right triangle, a²+b²=c².

Continue learning

Connected concepts

Curriculum references

Standards and instructional references

Illustrative Mathematics

Grade 8 scope, sequence, and public task structure

Coherent sequencing, representations, proof-oriented reasoning, and tasks.

Great Minds

Eureka Math² Grade 8 program structure

Module coherence, cumulative practice, and algebraic fluency.

Savvas Learning Company

enVision Mathematics Grade 8 instructional model

Problem-based entry points, visual learning, modeling, and application.

Common Core State Standards Initiative

Common Core State Standards for Mathematics — Grade 8

Grade-level content and mathematical-practice expectations.

California Mathematics Framework ↗

Math curriculum Next lesson →

Math V4 · Course chapter

Chapter 4: Transformations, Similarity, Pythagorean Geometry, and Volume

Geometry

Essential question: How can transformations and geometric relationships explain shape, distance, similarity, and measurement?

Where this lesson fits

Lesson 6 of 12. Each lesson builds on earlier chapter representations and ideas rather than resetting the topic.

Chapter destination

Build and defend a multi-representation model using transformations, similarity, pythagorean geometry, and volume, including interpretation, verification, and error analysis.

Learning objectives

What you should be able to do

Represent and solve understand similarity through transformations problems using precise mathematical notation, multiple representations, and justified reasoning.
Interpret and verify understand similarity through transformations results in context, including units, constraints, and reasonableness.

Prerequisite check

Make sure the foundation is ready.

Can you solve and explain prerequisite MAT-08-GEO-004 without relying on a memorized keyword?

Grade 8 uses this prerequisite as active knowledge in a more formal representation.

Learn

Build the idea from meaning, not memorization.

Chapter 4: Transformations, Similarity, Pythagorean Geometry, and Volume

Geometry. Lesson 6 of 12 extends earlier chapter reasoning.

Connection to the course

Use earlier Grade 8 chapters, Grade 7 prerequisite knowledge as active knowledge. Connect today's representation to at least one earlier representation and explain the relationship.

Meaning and structure

Understand Similarity Through Transformations belongs to geometry. Identify the governing property or relationship before choosing a procedure.

Multiple representations

Verification and interpretation

Math Box · Interactive lesson

Touch the math. Change it. See what stays true.

Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.

Transformation Lab

x2y3

(2, 3) → (4, 2)

Try these actions

Model understand similarity through transformations in the Math Box.
Change one input and predict which quantities or invariants should change.
Explain what the visual, equation, and numerical result say about the same relationship.

Worked examples

Twenty different ways to see the concept work.

Case 1: a figure is dilated by 2 then rotated. Similar?

yes

Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 2: a figure is dilated by 3 then rotated. Similar?

yes

A representation makes the mathematical structure visible before calculation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Explain why the method works, not only what steps to perform: Case 3: a figure is dilated by 4 then rotated. Similar?

yes

Justification connects each step to a definition, property, or relationship. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 4: a figure is dilated by 5 then rotated. Similar?

yes

An estimate provides an independent reasonableness check. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Verify the result with substitution, an inverse operation, or a second representation: Case 5: a figure is dilated by 6 then rotated. Similar?

yes

Independent verification should support the result without merely repeating the same procedure. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Interpret the result in context, including units, direction, rate, or geometric meaning: Case 6: a figure is dilated by 2 then rotated. Similar?

yes

Interpretation connects a computed value to the mathematical situation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 7: a figure is dilated by 3 then rotated. Similar?

Rigid transformations preserve size; dilations generally do not. Correct solution: yes

Error analysis identifies the broken idea and replaces it with valid reasoning. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Compare two related cases. Explain what changes and what remains mathematically consistent. Case A: Case 8: a figure is dilated by 4 then rotated. Similar? Case B: Case 19: a figure is dilated by 5 then rotated. Similar?

Case A: yes Case B: yes

Comparison should address structure and representation, not only numerical answers. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Case 9: a figure is dilated by 5 then rotated. Similar?

yes

Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 10: a figure is dilated by 6 then rotated. Similar?

yes

A representation makes the mathematical structure visible before calculation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Explain why the method works, not only what steps to perform: Case 11: a figure is dilated by 2 then rotated. Similar?

yes

Justification connects each step to a definition, property, or relationship. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 12: a figure is dilated by 3 then rotated. Similar?

yes

An estimate provides an independent reasonableness check. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Verify the result with substitution, an inverse operation, or a second representation: Case 13: a figure is dilated by 4 then rotated. Similar?

yes

Independent verification should support the result without merely repeating the same procedure. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Interpret the result in context, including units, direction, rate, or geometric meaning: Case 14: a figure is dilated by 5 then rotated. Similar?

yes

Interpretation connects a computed value to the mathematical situation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 15: a figure is dilated by 6 then rotated. Similar?

Rigid transformations preserve size; dilations generally do not. Correct solution: yes

Error analysis identifies the broken idea and replaces it with valid reasoning. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Compare two related cases. Explain what changes and what remains mathematically consistent. Case A: Case 16: a figure is dilated by 2 then rotated. Similar? Case B: Case 27: a figure is dilated by 3 then rotated. Similar?

Case A: yes Case B: yes

Comparison should address structure and representation, not only numerical answers. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Case 17: a figure is dilated by 3 then rotated. Similar?

yes

Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 18: a figure is dilated by 4 then rotated. Similar?

yes

A representation makes the mathematical structure visible before calculation. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Explain why the method works, not only what steps to perform: Case 19: a figure is dilated by 5 then rotated. Similar?

yes

Justification connects each step to a definition, property, or relationship. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 20: a figure is dilated by 6 then rotated. Similar?

yes

An estimate provides an independent reasonableness check. Dilation preserves angles and scales all lengths uniformly; rotation preserves shape.

Practice

Guided practice with hints

01Verify the result with substitution, an inverse operation, or a second representation: Case 21: a figure is dilated by 2 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: yes

02Interpret the result in context, including units, direction, rate, or geometric meaning: Case 22: a figure is dilated by 3 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: yes

03Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 23: a figure is dilated by 4 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: Rigid transformations preserve size; dilations generally do not. Correct solution: yes

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: Case A: yes Case B: yes

05Case 25: a figure is dilated by 6 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: yes

06Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 26: a figure is dilated by 2 then rotated. Similar?

Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.

Answer: yes

Practice

Independent practice

01Explain why the method works, not only what steps to perform: Case 27: a figure is dilated by 3 then rotated. Similar?

Answer: yes

02Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 28: a figure is dilated by 4 then rotated. Similar?

Answer: yes

03Verify the result with substitution, an inverse operation, or a second representation: Case 29: a figure is dilated by 5 then rotated. Similar?

Answer: yes

04Interpret the result in context, including units, direction, rate, or geometric meaning: Case 30: a figure is dilated by 6 then rotated. Similar?

Answer: yes

05Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 31: a figure is dilated by 2 then rotated. Similar?

Answer: Rigid transformations preserve size; dilations generally do not. Correct solution: yes

Answer: Case A: yes Case B: yes

07Case 33: a figure is dilated by 4 then rotated. Similar?

Answer: yes

08Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 34: a figure is dilated by 5 then rotated. Similar?

Answer: yes

Common mistakes

Learn to catch the error, not just the answer.

Assuming every transformation preserves size.

Rigid transformations preserve size; dilations generally do not.

Using the Pythagorean theorem on a non-right triangle.

a²+b²=c² applies to right triangles.

Applications & challenge

Use the idea beyond a single exercise.

Applications

Use transformations in design and coordinate geometry and Pythagorean reasoning for distance.
Model capacities of cylindrical, conical, and spherical objects.

Challenge problems

Explain why the method works, not only what steps to perform: Case 35: a figure is dilated by 6 then rotated. Similar?

yes

Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 36: a figure is dilated by 2 then rotated. Similar?

yes

Verify the result with substitution, an inverse operation, or a second representation: Case 37: a figure is dilated by 3 then rotated. Similar?

yes

Interpret the result in context, including units, direction, rate, or geometric meaning: Case 38: a figure is dilated by 4 then rotated. Similar?

yes

Flashcards

Retrieve it from memory.

Flashcards

Card 1 of 4

Game mode

Grade 8 Algebra & Modeling Sprint

Solve understand similarity through transformations problems and justify each result with a valid verification method.

Round 1 · Score 0Explain why the method works, not only what steps to perform: Case 35: a figure is dilated by 6 then rotated. Similar?

1 point for an accurate result and 1 point for a correct explanation or verification.

Practice

Mastery check

01Error analysis: a student says, "Assuming every transformation preserves size." Explain the error, then solve this related task correctly: Case 39: a figure is dilated by 5 then rotated. Similar?

Answer: Rigid transformations preserve size; dilations generally do not. Correct solution: yes

Answer: Case A: yes Case B: yes

03Case 41: a figure is dilated by 2 then rotated. Similar?

Answer: yes

04Represent the situation with a table, graph, diagram, number line, or equation before solving: Case 42: a figure is dilated by 3 then rotated. Similar?

Answer: yes

05Explain why the method works, not only what steps to perform: Case 43: a figure is dilated by 4 then rotated. Similar?

Answer: yes

06Estimate or predict the result first, then calculate and judge whether the answer is reasonable: Case 44: a figure is dilated by 5 then rotated. Similar?

Answer: yes

07Verify the result with substitution, an inverse operation, or a second representation: Case 45: a figure is dilated by 6 then rotated. Similar?

Answer: yes

08Interpret the result in context, including units, direction, rate, or geometric meaning: Case 46: a figure is dilated by 2 then rotated. Similar?

Answer: yes

Terminology

Words to know

transformation: A rule mapping a figure to an image.
congruent: Having the same size and shape.
similar: Having equal corresponding angles and proportional corresponding lengths.
Pythagorean theorem: For a right triangle, a²+b²=c².

Continue learning

Connected concepts

Curriculum references

Standards and instructional references

Illustrative Mathematics

Grade 8 scope, sequence, and public task structure

Coherent sequencing, representations, proof-oriented reasoning, and tasks.

Great Minds

Eureka Math² Grade 8 program structure

Module coherence, cumulative practice, and algebraic fluency.

Savvas Learning Company

enVision Mathematics Grade 8 instructional model

Problem-based entry points, visual learning, modeling, and application.

Common Core State Standards Initiative

Common Core State Standards for Mathematics — Grade 8

Grade-level content and mathematical-practice expectations.

California Mathematics Framework ↗

Math curriculum Next lesson →