Geometry 9-1 Complete Lesson: Translations

Solve It! Suppose you write the letters shown below on squares of tracing paper, so their shapes are visible from both sides.

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Solve It! How can you move the squares from HUM to get ICE?

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Solve It! How can you move the squares from bob to get pod?

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Vocabulary: Compare and contrast the geometric definition of transformation with its everyday English definition.

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Problem 1 Got It? Does the transformation appear to be a rigid motion? Explain.

Yes, the two figures appear to be congruent so the transformation seems to be a rigid motion.

Yes, the two figures are titled image and preimage so the transformation must be a rigid motion.

No, the two figures appear to be similar but not congruent so the transformation must not be a rigid motion.

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Problem 2 Got It?

A

B

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Problem 2 Got It?

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B

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Problem 3 Got It?
1. Copy △ABC onto the canvas in black.
2. Perform the translation below and graph the post-translation image in blue or green.
3. Draw these segments in red.

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Problem 4 Got It?

A

B

C

D

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Problem 5 Got It?

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A

B

C

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Graphing: Copy ▱NILE to the coordinate plane in black then graph its translation in blue or green.
Label vertices and include all relevant graph detail.

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A

B

C

D

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Vocabulary: What is true about a transformation that is not a rigid motion? Include a sketch of an example.

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Error Analysis: Your friend says the transformation △ABC →△PQR is a translation. Explain and correct her error.

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Reasoning: Write the translation as composition of a horizontal translation and a vertical translation.

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Review Lesson 8-1: Navigation: An airplane landed at a point 100 km east and 420 km south from where it took off. If the airplane flew in a straight line from where it took off to where it lands, how many kilometers did it fly? Enter only the number rounded to the nearest kilometer.

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Review Lesson 4-7: Proof: Complete the proof on the canvas.

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Review Lesson 3-8: The equations on the left go through a specific point A and are perpendicular to a specific line. Match each equation with its point A and equation of a perpendicular line on the right.

x = -1
y = -2
y = -x + 1

A(1, -2); x = -2
A(-1, -1); y = 1
A(-1, 2); y = x

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Vocabulary Review: Fill in the blanks to complete the sentence:
If two triangles are congruent, corresponding angle measures are the same/different and corresponding side lengths are the same/different.

the same; the same

the same; different

different; the same

different: different

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Respond with yes or no.

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Respond with yes or no.

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Enter only a number to represent the distance.

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Key Concept: Translation: Complete each sentence with the correct word from the left column.

some
all
change
preserve

Translations move __?__ points in a figure the same distance, in the same direction.
Translations __?__ side lengths of the figure.
Translations __?__ angle measures of the figure.

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Reflection: Math success

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Geometry 9-1 Complete Lesson: Translations

Solve It! How can you move the squares from HUM to get ICE?

Solve It! How can you move the squares from bob to get pod?

Vocabulary: Compare and contrast the geometric definition of transformation with its everyday English definition.

Problem 1 Got It? Does the transformation appear to be a rigid motion? Explain.

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? 1. Copy △ABC onto the canvas in black. 2. Perform the translation below and graph the post-translation image in blue or green. 3. Draw these segments in red.

Problem 4 Got It?

Problem 5 Got It?

Graphing: Copy ▱NILE to the coordinate plane in black then graph its translation in blue or green.Label vertices and include all relevant graph detail.

Vocabulary: What is true about a transformation that is not a rigid motion? Include a sketch of an example.

Error Analysis: Your friend says the transformation △ABC →△PQR is a translation. Explain and correct her error.

Reasoning: Write the translation as composition of a horizontal translation and a vertical translation.

Review Lesson 8-1: Navigation: An airplane landed at a point 100 km east and 420 km south from where it took off. If the airplane flew in a straight line from where it took off to where it lands, how many kilometers did it fly? Enter only the number rounded to the nearest kilometer.

Review Lesson 4-7: Proof: Complete the proof on the canvas.

Review Lesson 3-8: The equations on the left go through a specific point A and are perpendicular to a specific line. Match each equation with its point A and equation of a perpendicular line on the right.

Vocabulary Review: Fill in the blanks to complete the sentence:If two triangles are congruent, corresponding angle measures are the same/different and corresponding side lengths are the same/different.

Respond with yes or no.

Respond with yes or no.

Enter only a number to represent the distance.

Key Concept: Translation: Complete each sentence with the correct word from the left column.

Reflection: Math success

Solve It! How can you move the squares from HUM to get ICE?

Solve It! How can you move the squares from bob to get pod?

Vocabulary: Compare and contrast the geometric definition of transformation with its everyday English definition.

Problem 1 Got It? Does the transformation appear to be a rigid motion? Explain.

Problem 1 Got It? Does the transformation appear to be a rigid motion? Explain.

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? What are the vertices of the transformation? Select all that apply.

Problem 3 Got It? 1. Copy △ABC onto the canvas in black. 2. Perform the translation below and graph the post-translation image in blue or green. 3. Draw these segments in red.

Problem 3 Got It? Reasoning: Consider the segments you drew in step 3 of the previous item. What relationships exist among these three segments? Select all that apply.

Problem 4 Got It?

Problem 5 Got It?

Graphing: Copy ▱NILE to the coordinate plane in black then graph its translation in blue or green.Label vertices and include all relevant graph detail.

Vocabulary: What is true about a transformation that is not a rigid motion? Include a sketch of an example.

Error Analysis: Your friend says the transformation △ABC →△PQR is a translation. Explain and correct her error.

Reasoning: Write the translation as composition of a horizontal translation and a vertical translation.

Review Lesson 8-1: Navigation: An airplane landed at a point 100 km east and 420 km south from where it took off. If the airplane flew in a straight line from where it took off to where it lands, how many kilometers did it fly? Enter only the number rounded to the nearest kilometer.

Review Lesson 4-7: Proof: Complete the proof on the canvas.

Review Lesson 3-8: The equations on the left go through a specific point A and are perpendicular to a specific line. Match each equation with its point A and equation of a perpendicular line on the right.

Vocabulary Review: Fill in the blanks to complete the sentence:If two triangles are congruent, corresponding angle measures are the same/different and corresponding side lengths are the same/different.

Respond with yes or no.

Respond with yes or no.

Enter only a number to represent the distance.

Key Concept: Translation: Complete each sentence with the correct word from the left column.

Reflection: Math success

Problem 1 Got It? Does the transformation appear to be a rigid motion? Explain.

Problem 3 Got It? What are the vertices of the transformation? Select all that apply.

Problem 3 Got It? Reasoning: Consider the segments you drew in step 3 of the previous item. What relationships exist among these three segments? Select all that apply.

Problem 3 Got It?
1. Copy △ABC onto the canvas in black.
2. Perform the translation below and graph the post-translation image in blue or green.
3. Draw these segments in red.

Graphing: Copy ▱NILE to the coordinate plane in black then graph its translation in blue or green.
Label vertices and include all relevant graph detail.

Vocabulary Review: Fill in the blanks to complete the sentence:
If two triangles are congruent, corresponding angle measures are the same/different and corresponding side lengths are the same/different.

Problem 3 Got It? What are the vertices of the transformation?
Select all that apply.

Problem 3 Got It?
1. Copy △ABC onto the canvas in black.
2. Perform the translation below and graph the post-translation image in blue or green.
3. Draw these segments in red.

Graphing: Copy ▱NILE to the coordinate plane in black then graph its translation in blue or green.
Label vertices and include all relevant graph detail.

Vocabulary Review: Fill in the blanks to complete the sentence:
If two triangles are congruent, corresponding angle measures are the same/different and corresponding side lengths are the same/different.

Problem 3 Got It? What are the vertices of the transformation?
Select all that apply.