Unit 1, Lesson 1: Moving in the Plane · Unit 1, Lesson 2: Naming the Moves 1.Each of the six cards shows a shape. a.Which pair of cards shows a shape and its image after a rotation?

Unit 1, Lesson 1: Moving in the Plane1. The six frames show a shape's different positions.

Describe how the shape moves to get from its position in each frame to the next.

2. These five frames show a shape's different positions.


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Unit 1: Rigid Transformations and Congruence Lesson 1: Moving in the Plane 1

3. Diego started with this shape.

Diego moves the shape down, turns it 90 degrees clockwise, then moves the shape to the right. Drawthe location of the shape after each move.

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Unit 1: Rigid Transformations and Congruence Lesson 1: Moving in the Plane 2

Unit 1, Lesson 2: Naming the Moves1. Each of the six cards shows a shape.

a. Which pair of cards shows a shape and its image after a rotation?

b. Which pair of cards shows a shape and its image after a reflection?

2. The five frames show a shape's different positions.


3. The rectangle seen in Frame 1 is rotated to a new position, seen in Frame 2.

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Unit 1: Rigid Transformations and Congruence Lesson 2: Naming the Moves 1

Select all the ways the rectangle could have been rotated to get from Frame 1 to Frame 2.

A. 40 degrees clockwise

B. 40 degrees counterclockwise

C. 90 degrees clockwise

D. 90 degrees counterclockwise

E. 140 degrees clockwise

F. 140 degrees counterclockwise

(from Unit 1, Lesson 1)

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Unit 1: Rigid Transformations and Congruence Lesson 2: Naming the Moves 2

Unit 1, Lesson 3: Grid Moves1. Apply each transformation described to Figure A. If you get stuck, try using tracing paper.

a. A translation which takes tob. A counterclockwise rotation of A, using center , of 60 degreesc. A reflection of A across line

2. Here is triangle drawn on a grid.

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Unit 1: Rigid Transformations and Congruence Lesson 3: Grid Moves 1

3. a. Draw the translated image of so that vertex moves to . Tracing paper may be useful.

b. Draw the reflected image of Pentagon with line of reflection . Tracing paper may beuseful.

c. Draw the rotation of Pentagon around clockwise by an angle of 150 degrees. Tracing

On the grid, draw a rotation of triangle , a translationof triangle , and a reflection of triangle .Describe clearly how each was done.

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paper and a protractor may be useful.


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Unit 1, Lesson 4: Making the Moves1. For each pair of polygons, describe a sequence of translations, rotations, and reflections that takes

Polygon P to Polygon Q.

a.

b.

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Unit 1: Rigid Transformations and Congruence Lesson 4: Making the Moves 1

c.

2. Here is quadrilateral and line .

Draw the image of quadrilateral after reflecting it across line .


3. Here is quadrilateral .

Draw the image of quadrilateral after each rotation using as center.

a. 90 degrees clockwise

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b. 120 degrees clockwisec. 30 degrees counterclockwise


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Unit 1, Lesson 5: Coordinate Moves1. a. Here are some points.

What are the coordinates of , , and after a translation to the right by 4 units and up 1 unit?Plot these points on the grid, and label them , and .

b. Here are some points.

What are the coordinates of , , and after a reflection over the axis? Plot these points on thegrid, and label them , and .

c. Here are some points.

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Unit 1: Rigid Transformations and Congruence Lesson 5: Coordinate Moves 1

What are the coordinates of , , and after a rotation about by 90 degrees clockwise? Plotthese points on the grid, and label them , and .

2. Describe a sequence of transformations that takes trapezoid A to trapezoid B.


3. Reflect polygon using line .

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Unit 1, Lesson 6: Describing Transformations1. Here is Trapezoid A in the coordinate plane:

a. Draw Polygon B, the image of A, using the -axis as the line of reflection.b. Draw Polygon C, the image of B, using the -axis as the line of reflection.c. Draw Polygon D, the image of C, using the -axis as the line of reflection.

2. The point is rotated 180 degrees counterclockwise using center . What are thecoordinates of the image?

A.B.C.D.

3. Describe a sequence of transformations for which Triangle B is the image of Triangle A.

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Unit 1: Rigid Transformations and Congruence Lesson 6: DescribingTransformations

1

4. Here is quadrilateral .

Draw the image of quadrilateral after each transformation.

a. The translation that takes to .

b. The reflection over segment .

c. The rotation about point by angle , counterclockwise.


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Unit 1: Rigid Transformations and Congruence Lesson 6: DescribingTransformations

2

Unit 1, Lesson 7: No Bending or Stretching1. Is there a rigid transformation taking Rhombus P to Rhombus Q? Explain how you know.

2. Describe a rigid transformation that takes Triangle A to Triangle B.

3. Is there a rigid transformation taking Rectangle A to Rectangle B? Explain how you know.

4. For each shape, draw its image after performing the transformation. If you get stuck, consider usingtracing paper.

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Unit 1: Rigid Transformations and Congruence Lesson 7: No Bending orStretching

1

a. Translate the shape so that goesto .

b. Rotate the shape 180 degreescounterclockwise around .

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2


c. Reflect the shape over the lineshown.

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Unit 1, Lesson 8: Rotation Patterns1. For the figure shown here,

a. Rotate segment around point .b. Rotate segment around point .c. Rotate segment around point .

2. Here is an isosceles right triangle:

3. Each graph shows two polygons and . In each case, describe a sequence oftransformations that takes to .

a.

Draw these three rotations oftriangle together.

a. Rotate triangle 90degrees clockwise around

.b. Rotate triangle 180

degrees around .c. Rotate triangle 270

degrees clockwise around.

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Unit 1: Rigid Transformations and Congruence Lesson 8: Rotation Patterns 1

b.


4. Lin says that she can map Polygon A to Polygon B using only reflections. Do you agree with Lin?Explain your reasoning.


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Unit 1: Rigid Transformations and Congruence Lesson 8: Rotation Patterns 2

Unit 1, Lesson 9: Moves in Parallel1. a. Draw parallel lines and .

b. Pick any point . Rotate 90 degrees clockwise around .c. Rotate 90 degrees clockwise around .d. What do you notice?

2. Use the diagram to find the measures of each angle. Explain your reasoning.

3. Points and are plotted on a line.

a.b.c.

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Unit 1: Rigid Transformations and Congruence Lesson 9: Moves in Parallel 1

4. In the picture triangle is an image of triangle after a rotation. The center of rotation is .

a. What is the length of side ? Explain how you know.

b. What is the measure of angle ? Explain how you know.

c. What is the measure of angle ? Explain how you know.


5. The point is rotated 180 degrees counterclockwise using center . What are the coordinates

a. Find a point so that a 180-degree rotation withcenter sends to and to .

b. Is there more than one point that works for part a?

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of the image?

A.B.C.D.


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Unit 1, Lesson 10: Composing Figures1. Here is the design for the flag of Trinidad and Tobago.

Describe a sequence of translations, rotations, and reflections that take the lower left triangle to theupper right triangle.

2. Here is a picture of an older version of the flag of Great Britain. There is a rigid transformation thattakes Triangle 1 to Triangle 2, another that takes Triangle 1 to Triangle 3, and another that takesTriangle 1 to Triangle 4.

a. Measure the lengths of the sides in Triangles 1 and 2. What do you notice?

b. What are the side lengths of Triangle 3? Explain how you know.

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Unit 1: Rigid Transformations and Congruence Lesson 10: Composing Figures 1

c. Do all eight triangles in the flag have the same area? Explain how you know.

3. a. Which of the lines in the picture is parallel to line ? Explain how you know.

b. Explain how to translate, rotate or reflect line to obtain line .

c. Explain how to translate, rotate or reflect line to obtain line .


4. Point has coordinates . After a translation 4 units left, a reflection across the -axis, and atranslation 2 units down, what are the coordinates of the image?


5. Here is triangle :

Draw these three rotations of triangle together.

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a. Rotate triangle 90 degrees clockwise around .b. Rotate triangle 180 degrees around .c. Rotate triangle 270 degrees clockwise around .


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Unit 1, Lesson 11: What Is the Same?1. If two rectangles have the same perimeter, do they have to be congruent? Explain how you know.

2. Draw two rectangles that have the same area, but are not congruent.

3. For each pair of shapes, decide whether or not it appears that the two shapes are congruent. Explainyour reasoning.

a.

b.

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Unit 1: Rigid Transformations and Congruence Lesson 11: What Is the Same? 1

4. a. Reflect Quadrilateral A over the -axis. Label the image quadrilateral B. Reflect Quadrilateral Bover the -axis. Label the image C.

b. Are Quadrilaterals A and C congruent? Explain how you know.

5. The point is rotated 90 degrees counterclockwise using center . What are the coordinatesof the image?

A.B.C.D.


6. Describe a rigid transformation that takes Polygon A to Polygon B.

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Unit 1, Lesson 12: Congruent Polygons1. a. Show that the two pentagons are congruent.

b. Find the side lengths of and the angle measures of .

2. For each pair of shapes, decide whether or not the two shapes are congruent. Explain your reasoning.

a.

b.

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Unit 1: Rigid Transformations and Congruence Lesson 12: Congruent Polygons 1

c.

3. a. Draw segment .

b. When is rotated around point , the resulting segment is the same as . Where couldpoint be located?


4. Here is trapezoid .

Using rigid transformations on the trapezoid, build a pattern. Describe some of the rigidtransformations you used.


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Unit 1: Rigid Transformations and Congruence Lesson 12: Congruent Polygons 2

Unit 1, Lesson 13: Congruence1. Which of these four figures are congruent to the top figure?

2. These two figures are congruent, with corresponding points marked.

a. Are angles and congruent? Explain your reasoning.

b. Measure angles and to check your answer.

3. Here are two figures.

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Unit 1: Rigid Transformations and Congruence Lesson 13: Congruence 1

Show, using measurement, that these two figures are not congruent.

4. Each picture shows two polygons, one labeled Polygon A and one labeled Polygon B. Describe how tomove Polygon A into the position of Polygon B using a transformation.

a.

b.

c.

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Unit 1, Lesson 14: Alternate Interior Angles1. Use the diagram to find the measures of each angle. Explain your reasoning.


2. Lines and are parallel, and the measure of angle is 19 degrees.

a. Explain why the measure of angle is 19 degrees. If you get stuck, consider translating lineby moving to .

b. What is the measure of angle ? Explain.

3. The diagram shows three lines with some marked angle measures.

a.b.c.

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Unit 1: Rigid Transformations and Congruence Lesson 14: Alternate InteriorAngles

1

Find the missing angle measures marked with question marks.

4. The two figures are scaled copies of each other.

a. What are some ways that you can tell they are scaled copies?

b. What is the scale factor that takes Figure 1 to Figure 2?

c. What is the scale factor that takes Figure 2 to Figure 1?

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Unit 1: Rigid Transformations and Congruence Lesson 14: Alternate InteriorAngles

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Unit 1, Lesson 15: Adding the Angles in a Triangle1. In triangle , the measure of angle is .

a. Give possible measures for angles and if triangle is isosceles.b. Give possible measures for angles and if triangle is right.

2. For each set of angles, decide if there is a triangle whose angles have these measures in degrees:

a. 60, 60, 60b. 90, 90, 45c. 30, 40, 50d. 90, 45, 45e. 120, 30, 30

If you get stuck, consider making a line segment. Then use a protractor to measure angles with thefirst two angle measures.

3. Angle in triangle is obtuse. Can angle or angle be obtuse? Explain your reasoning.

4. For each pair of polygons, describe the transformation that could be applied to Polygon A to getPolygon B.

a.

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Unit 1: Rigid Transformations and Congruence Lesson 15: Adding the Angles ina Triangle

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b.

c.


5. On the grid, draw a scaled copy of quadrilateral using a scale factor of .

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Unit 1, Lesson 16: Parallel Lines and the Angles in aTriangle

1. For each triangle, find the measure of the missing angle.

2. Is there a triangle with two right angles? Explain your reasoning.

3. In this diagram, lines and are parallel.

Angle measures and angle measures .

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Unit 1: Rigid Transformations and Congruence Lesson 16: Parallel Lines andthe Angles in a Triangle

1

a. What is ?b. What is ?c. What is ?

4. The two figures are congruent.

a. Label the points , and that correspond to , , and in the figure on the right.

b. If segment measures 2 cm, how long is segment ? Explain.

c. The point is shown in addition to and . How can you find the point that corresponds to? Explain your reasoning.

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Unit 1, Lesson 1: Moving in the Plane · Unit 1, Lesson 2: Naming the Moves 1.Each of the six cards shows a shape. a.Which pair of cards shows a shape and its image after a rotation?