Geometry: Unit 3

Unit 3 – Item 1

1

A regular pentagon is rotated 90 degrees counterclockwise around the origin, reflected over the
𝑦 = 𝑥 line and translated 1 unit up and 1 unit to the right. Which quadrant would a majority of the
points fall?

1

Unit 3 – Item 2
Which of the following options best describes the relationship between the criteria for triangle congruence (SAS and ASA) and the definition of congruence in terms of rigid motions, emphasizing the fundamental connections between transformations and the establishment of congruent triangles? Choose the best response.

Unit 3 – Item 3
Explain why you agree or disagree with each of Alan's statements below.

1

Allan stated reflection was the single transformation applied to get from triangle A to triangle B

1

Alan states triangle A is neither similar nor congruent to triangle B

1

Alan stated dilated shapes can sometimes show congruence

Unit 3 – Item 4
Graph the image and the preimage of the figure using the series of transformations given: C(2, −3), V(3, 1), R(5, −2)

1

Translation: (x, y)→(x−5, y+4)

Instructions

Click the graph tab.
Choose the correct graph type.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

Linear

1

Reflection: (x, y)→(y, x)

Instructions

Click the graph tab.
Choose the correct graph type.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

Linear

1

Rotation: (x, y)→(-x, -y)

Instructions

Click the graph tab.
Choose the correct graph type.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

Linear

1

Unit 3 – Item 5
Imagine two identical triangular garden plots are being planned for a community project. How can you ensure that both plots are exactly the same shape and size using geometric principles?

1

Unit 3 – Item 6
You are creating a mural that includes geometric shapes, including triangles. How would you
ensure that two triangles in your mural are congruent? Use transformations and geometric
reasoning to explain.

1

Unit 3 – Item 7
Which transformation changes the orientation of a figure without changing its size or shape? Choose the best answer.

Unit 3 – Item 8

1

Part A
Describe the transformation(s) that would cause the black letter to get to the blue letter.

1

Part B

Are the two letters congruent? Explain how you know, using words such as, line segment and angle.

1

Unit 3 – Item 9
Connect each definition to the transformation which it describes.

Draggable item		Corresponding Item
Dilation		A transformation that slides a figure from one position to another without rotating it.
Rotation		A transformation that turns a figure around a fixed point
Translation		A transformation that flips a figure over a line called the line of reflection
Reflection		A transformation that enlarges or reduces the size of a figure

1

Unit 3 – Item 10
A regular hexagon is rotated 60 degrees counterclockwise around its center. Which geometric properties remain unchanged after this rotation? Choose all that apply.

A regular pentagon is rotated 90 degrees counterclockwise around the origin, reflected over the𝑦 = 𝑥 line and translated 1 unit up and 1 unit to the right. Which quadrant would a majority of thepoints fall?

Allan stated reflection was the single transformation applied to get from triangle A to triangle B

Alan states triangle A is neither similar nor congruent to triangle B

Alan stated dilated shapes can sometimes show congruence

Translation: (x, y)→(x−5, y+4)

Reflection: (x, y)→(y, x)

Rotation: (x, y)→(-x, -y)

Unit 3 – Item 5Imagine two identical triangular garden plots are being planned for a community project. How can you ensure that both plots are exactly the same shape and size using geometric principles?

Unit 3 – Item 6You are creating a mural that includes geometric shapes, including triangles. How would youensure that two triangles in your mural are congruent? Use transformations and geometricreasoning to explain.

Unit 3 – Item 7Which transformation changes the orientation of a figure without changing its size or shape? Choose the best answer.

Part ADescribe the transformation(s) that would cause the black letter to get to the blue letter.

Part BAre the two letters congruent? Explain how you know, using words such as, line segment and angle.

Unit 3 – Item 9Connect each definition to the transformation which it describes.

Unit 3 – Item 10A regular hexagon is rotated 60 degrees counterclockwise around its center. Which geometric properties remain unchanged after this rotation? Choose all that apply.

A regular pentagon is rotated 90 degrees counterclockwise around the origin, reflected over the
𝑦 = 𝑥 line and translated 1 unit up and 1 unit to the right. Which quadrant would a majority of the
points fall?

Unit 3 – Item 5
Imagine two identical triangular garden plots are being planned for a community project. How can you ensure that both plots are exactly the same shape and size using geometric principles?

Unit 3 – Item 6
You are creating a mural that includes geometric shapes, including triangles. How would you
ensure that two triangles in your mural are congruent? Use transformations and geometric
reasoning to explain.

Unit 3 – Item 7
Which transformation changes the orientation of a figure without changing its size or shape? Choose the best answer.

Part A
Describe the transformation(s) that would cause the black letter to get to the blue letter.

Part B

Are the two letters congruent? Explain how you know, using words such as, line segment and angle.

Unit 3 – Item 9
Connect each definition to the transformation which it describes.

Unit 3 – Item 10
A regular hexagon is rotated 60 degrees counterclockwise around its center. Which geometric properties remain unchanged after this rotation? Choose all that apply.