Lesson #13 Congruence, Symmetry and …acpssharepoint.appomattox.k12.va.us/AMS/amsteams/amsencore...Transformations: Translations, Reflections, and Rotations ... creates an image from

Math Buddies -Grade 4 13-1

Lesson #13

Congruence, Symmetry and

Transformations: Translations, Reflections, and Rotations

Goal:

• Identify congruent and noncongruent figures

• Recognize the congruence of plane figures resulting from geometric transformations such as

translation (slide), reflection (flip) and rotation (turn).

• Identify figures that are symmetric and lines of symmetry

Vocabulary:

• Congruent figures have the same size and shape. The angles and line segments that make

up the plane figure are exactly the same size and shape. Two shapes or solids are congruent if

they are identical in every way except for their position; one can be turned into the other by

rotation, reflection or translation.

• A figure or shape is Symmetrical when one-half of the figure is the mirror image of the

other half

• A Line of Symmetry divides a symmetrical figure, object, or arrangement of objects into

two parts that are congruent if one part is reflected (flipped) over the line of symmetry

• Transformation is an operation that creates an image from an original figure or pre-image.

Translations, Reflections and Rotations are some of the transformations on the plane.

Although there is a change in position for the original figure, there is no change to the shape

or size of the original figure.

• Translation (Slide) is a transformation of an object that means to move the object without

rotating or reflecting it. Every translation has a given direction and a given distance.

• Reflection (Flip) is a transformation of an object that means to produce its mirror image of

the object on the opposite side of a line. Every reflection has a mirror line or a line of

reflection. A reflection of an "R" is a backwards "R"

• Rotation (Turn) is a transformation of an object that means to turn it around a given

point, called the center. Every rotation has a center of rotation, an angle of rotation,

and a direction (counterclockwise and clockwise).

• Tessellations are patterns of shapes that cover a plane without gaps (holes) or

overlaps are called tessellations.

Related SOL: 4.17 The student will

b) identify congruent and noncongruent shapes; and

c) investigate congruence of plane figures after geometric transformations such as

reflection (flip), translation (slide) and rotation (turn), using mirrors, paper folding, and

tracing.


Materials:

• 2 Mira

• Sheets of Patty Paper

• 50 assorted Pattern Block Pieces

• 1 set of colored pencils

• 2 Sets of Tangrams (7 piece Chinese puzzle)

• Translation, Reflection and Rotation Concentration Cards (20)

Goal 1: Recognize congruent and non-congruent plane figures

Activity 1.1: Warm-Up: Congruent Object Search

1. Say: Look around the room. Can anyone identify two objects or figures that appear to

be exactly alike? (Answers will vary) 2. Say: Lets look at these two objects (or figures). How many sides do the objects have?

How many angles do the objects have? Are the shapes the same size? Do they have the

same shape?

3. Say: Congruent figures have the same size and shape. Would you say these two objects

(or figures) are congruent?

4. Say: To further explain congruence, think about going to your favorite mall and looking

at dozens of copies of your favorite CD on sale. All of the CDs are exactly the same size

and shape. In fact, you can probably think of many objects that are mass-produced to

be exactly the same size and shape. Congruent objects are exactly the same- they are

duplicates of one another. In Mathematics, if two figures are congruent and you cut

one figure out with a pair of scissors, it would fit perfectly on top of the other figure.

So, if two quadrilaterals (4 sided) are the same size and shape, they are congruent. If

two pentagons (5 sided) are the same size and shape, they are congruent.

5. Say: Now, let’s hear from you. Would you please describe what a pair of congruent

objects or figures have in common? Students might suggest that congruent figures have the

same size and shape. The angles and line segments that make up the congruent figures are

exactly the same size and shape. Say: Yes, congruent figures have the same size and

shape.

6. Say: Look around the room and see if you can identify two other objects in the

classroom that are congruent. What did you find? Wait for answers. After the math

buddies have chosen two objects, say: Can you explain to us why the objects are

congruent?

7. Ask the following leading questions to guide the students in a discussion as to why the

congruent figures are congruent. Depending on the objects, ask:

• How many sides do the shapes have? • How many angles do the shapes have? • How can you tell that the shapes the same size?


• How do you know these are the same shapes? • When we say two objects are congruent, does the color of

the shape matter? (no) 8. Say: On paper, draw this symbol .

Say: The mathematical symbol used to denote congruent is .

The symbol is made up of two parts:

~ which means the same shape (similar) and

= which means the same size (equal).

Activity 1.2: Congruent or Not 1. Say: Open your book to Lesson #13: Student Activity Sheet #1:Congruent or Not. Look

at the various shapes and determine whether they are congruent. Put a check under yes

or no to indicate your answer. Then explain why they are or are not congruent.

2. Answers: 1. No, not the same size. 2. Yes, even though one is shaded. 3. No, different size

and shaped triangles. 4. Yes, lines don’t change the shape or size. 5. No, different size. 6.

Yes, different position but the same shape and size.

Activity 1.2: Tantalizing Triangles 1. Say: We can further refine our definition of congruent figure by saying that two shapes

or solids are congruent if they are identical in every way except for their position; a

figure can be moved by slides, flips or turns, and still be congruent.

2. Open the set of colored pencils for the Math Buddies to use and give each student one piece

of patty paper to use as tracing paper. Say: Open your book to Lesson #13: Student

Activity Sheet #2: Tantalizing Triangles. The objective of this activity is to find the

tantalizing triangles that are congruent. To determine if they are congruent, carefully

trace one of the triangles and then move the traced triangle around the page to find

others that are congruent to it. Remember it does not matter what position the shape is

in relative to another shape. Color any congruent triangles you find with the same color

pencil. Then trace a second triangle and continue the same process. There are four

different shaped triangles and all triangles should be colored. Good luck!

Answers: Set #1: A, E, N, K are congruent

Set #2: D, I, M, P are congruent

Set #3: C, J, H, L are congruent

Set #4: B, G, O, F are congruent

Goal 2: Recognize the congruence of plane figures resulting from

geometric transformations such as reflection (flip),

translation (slide), and rotation (turn).

Activity 2.1: Warm-Up: Transformations with Tangrams

1. Describing figures and visualizing what they look like when they are transformed through

translations (slides), reflections (flips), and rotations (turns), or when they are put together or

Congruent

Symbol


taken apart in different ways are important aspects of the geometry program in elementary

school. In this activity, students will use the seven tangram pieces to explore the

transformation of shapes as they work to solve a few tangram puzzles. The potential for a

high-quality spatial visualization experiences provided this activity that involves the use of

manipulatives should enhance student understanding of transformations. The manipulative to

be used is Tangrams, which are an ancient Chinese moving piece puzzle, consisting of 7

geometric shapes.

2. Give each student a set of tangrams and say: This is a set of seven tangram pieces from the

ancient Chinese puzzle. The Tangram shapes were used for recreational activity in

China thousands of years ago. The word Tangram is derived from tan, meaning

Chinese, and gram, meaning diagram or arrangement. Spread them out on the table

and point to the pieces as I say them: the square, two small triangles, one medium

triangle, two large triangles, and one parallelogram.

3. Say: Let’s examine each of the five different Tangram pieces, and determine the area of

each piece, assuming that the small triangle has an area of one unit. Answers

Small Triangle 1 square unit

Square 2 square units

Parallelogram 2 square units

Medium Triangle 2 square unit

Large Triangle 4 square unit

4. Say: You can use all seven pieces to make a figure or your can use a given number to

make a figure. We are going to make a square of different sizes using a defined number

of pieces. Let’s try these tasks together. Select one or more based upon time constraints.

Possible solutions follow. • Can you make a square using one piece? (use the square piece)

• Can you make a square using two pieces? (two small triangles or two large

triangles)

• Can you make a square using three pieces? (two small triangles and one medium

triangle)

• Can you make a square using four pieces?

• Can you make a square using five pieces?

• Note: Using six pieces can’t be done

• Can you make a square using seven pieces? (see below)


5. Say: Please use the seven tangram pieces to make one of the figures you select on

Lesson#20: Student Activity Sheets #3A or #3B. You must use all seven pieces for each

figure. I will check your answers once you inform me that you have completed a figure. 6. Answers:

Activity 2.2: Transformations: Translations (Slides) 1. Say: You have been working with the Tangram pieces. While you worked to

manipulate the shapes to create the different figures, often you were visualizing what

they would look like once you had transformed them. You had a chance to move

around the tangram pieces using a variety of transformations.

2. Say: “Transformations” is a word used to describe a category of movements that you

can make with a shape. We will be studying three transformations: translations,

rotations, and reflections.

3. Take out Lesson #13: Teacher Sheet #1. Refer to the top of the sheet as you describe

translation transformations. Say: Translations are like slides, like sliding down a

playground slide where you move from high to low but you are still sitting upright

when you hit the bottom. A translation "slides" an object a fixed distance in a given

direction. The original object and its translation have the same shape and size, and

they face in the same direction. [Note: The word "translate" in Latin means "carried

across".] When you are sliding down a water slide, you are experiencing a translation.

Your body is moving a given distance (the length of the slide) in a given direction. You

do not change your size, shape or the direction in which you are facing. Translations

can be seen in wallpaper designs, textile patterns, mosaics, and artwork.

4. Say: Open your student books to Lesson #13: Student Activity Sheet #4. Look at the

pentagons (five sided figures) at the top left hand side of the page. In mathematics, the

translation of an object is called its image. If the original object was labeled with

letters, such as ABCDE, the image may be labeled with the same letters followed by a

prime symbol (like an apostrophe), A'B'C'D'E'.


Think of

polygon

ABCDE as

sliding two

inches to the

right and one

inch down. Its

new position is

labeled

A'B'C'D'E'.

5. Say: A translation moves an object without changing its size or shape and without

turning it or flipping it. Take out the Pattern Blocks and say: Here are some pattern

blocks. Take out a blue parallelogram, a green triangle and a red trapezoid. On the

pattern block grid paper, draw the translations of each shape by first placing it on the

original figure and then sliding the pattern blocks the distance and the direction

indicated by the arrow. To simplify this process we have only labeled one vertex of the

shape with a letter. The image of the shape should have the same letter followed by the

prime symbol in its new position as it had in it’s original position. Check for accuracy of

drawing. Ask: Did your shapes look different as a result of your translations? (no they

do not change size or shape, just position)

6. Say: Now look at Part B on Activity Sheet #4. For each of the four problems, check yes

or no to indicate whether one figure is the translation of the other.

7. Answers:

1. yes 2. no (change in size) 3. yes (doesn’t need a slide line) 4. yes

Activity 2.3: Transformations: Rotations (Turns) 1. Again take out Lesson #13: Teacher Sheet #1. Refer to the middle of the sheet as you

describe the rotation transformation. Say: Rotations are turns, like when a basketball

player pivots on one foot, or when a Ferris wheel turns around the center of the wheel.

Look at this picture on the teacher page. To rotate a shape, you need to identify three

things. First you must identify the point around which you are turning the shape, called

the center of rotation. Second, you need to know the direction of the turn, clockwise or

counterclockwise. Third, you need to know the angle, the number of degrees of the

turn, or the fractional part of 1 whole turn (e.g. turn, or turn). Notice that the

picture displays a clockwise rotation of the “R” around a center point, and where the

angle of the turn is 90 degrees, or a one-quarter turn.

2. Say: Open your student books to Lesson #13: Student Activity Sheet #5: Discover

Rotation. Notice the letter “B” being rotated four times around the center of the two

intersecting lines. What is the direction of the rotation, clockwise or counterclockwise?

(clockwise) What is the angle of the rotation for each turn? (90 degrees, or a one-

quarter turn) You might think of a rotation like putting an object on a plate or a “Lazy


Susan”, and then spinning the plate (or “Lazy Susan”) around while the plate's center

(or “Lazy Susan’s” center) stays in one place. The center of the object doesn't have to

be at the center of rotation (i.e. the center of your plate). Any point can be used to mark

the center of rotation.

3. Say: Now look at the pattern block arrangement. Using the pattern blocks, make this

same arrangement on the left side of a piece of paper. Wait until made Now, move this

pattern block arrangement in a clockwise direction for an angle of 90 degrees or of a

turn. Did it move off the paper? (yes) Did you arrangement stay the same distance from

the center of rotation which is the bottom left hand corner of the paper as it was when

you first made it? (yes)

4. Say: Now open your student books to Lesson #13: Student Activity Sheet #6: Rotation

and Reflection With Pattern Blocks. In Part A, I would like Math Buddy A to make a

pattern block figure on line A. Once the pattern is complete, I would like Math Buddy

B to make this same pattern block figure on line B showing the pattern after a one-

quarter rotation in a clockwise direction. Wait until this is complete. Ask: Take a look at

your work. Do you think it represents a clockwise rotation of 90 degrees and that the

figures are an equal distance from the center of rotation? If not, what must be

changed? If yes, you have demonstrated a rotation.

5. Say: In Summary, how can a rotation of an object be described? (There are three

essential parts: 1)the object must move in a direction, clockwise or counterclockwise; 2) the

object must move around a point called the center of rotation; and the object must turn some

number of degrees or a fractional part of 1 whole turn.)

6. Say: Now, go back to the bottom of Student Activity Sheet #5. Decide which of the four

problems represent rotations and which are not.

Answers: 1. yes (1/4 turn clockwise) 2. yes (3/4 turn clockwise, or turn

counterclockwise) 3. No, a translation 4. Yes (1/2 turn clockwise, or turn

counterclockwise)

Activity 2.4: Transformations: Reflections (Flips)

1. Take out Lesson #13: Teacher Sheet #1. Refer to the third transformation called reflection.

Say: Reflection is the third transformation we will study. Reflections are like flips: like

the picture of a gymnast doing a handstand. Look at the happy face and the “R” on

this page. Each has been reflected across a line of reflection.

2. Say: In the real world, a reflection can be seen in water, in a mirror, in glass, or in a

shiny surface. An object and its reflection have the same shape and size, but the figures

face in opposite directions.

3. Say: When you look in the mirror what do you notice that is the same and is different

about your face? (Discuss answers) In a mirror, right and left are switched. Under a

reflection in a mirror, the figure does not change size. It is simply flipped over the line

of reflection. In mathematics, the reflection of an object is called its image.


4. Say: Now open your student books to Lesson #13: Student Activity Sheet #6: Rotation

and Reflection With Pattern Blocks. At the bottom of the page in Part B, I would like

Math Buddy A to place a red trapezoid on the left side of the line, touching the line.

Once the trapezoid is placed, say: Now, I would like Math Buddy B to place a red

trapezoid on the right side of the line to show a reflection of this pattern block. Does

everyone agree that this is the reflection image of the pattern block on the left. If not,

make the corrections. This is one example; other placements of the trapezoid lead to other

arrangements.

Line of Reflection

Reflection – Image of Reflection

5. Say: Now let’s try a more challenging task. At the bottom of the page in Part B, I would

like Math Buddy A to make a pattern block design on the left side of the line so that the

design touches the line. Once the pattern design is complete, I would like Math Buddy

B to make the reflection of this pattern block design on the right side of the line to show

the designs reflection. Once complete, say: Does everyone agree that this is the reflection

of the pattern block design across the line of reflection? Do we need to make any

corrections?

6. Say: Now, switch rolls, and Math Buddy B will create the design on the right side, and

Math Buddy A will create it’s reflection on the left side. Once complete, say: Does

everyone agree that this is the reflection of the pattern block design across the line of

reflection? Do we need to make any corrections?

Activity 2.5: Rotation or Reflection? 1. Say: Now open your student books to Lesson #13: Student Activity Sheet #7: Rotation

or Reflection? Here is a table of figures. Use your knowledge to decide whether the

second figure, the image, is a rotation or a reflection of the first. Once you decide,

check under the column heading of this transformation. Some images may represent a

rotation and a reflection, so check both.

2. Answers: 1. Rotation (1/4 turn) 2. Reflection (across a horizontal line) or Rotation (1/2

turn) 3. Reflection (across a vertical line) 4. Rotation (3/4 turn clockwise; or turn

counterclockwise) 5. Rotation (1/4 turn clockwise) 6. Reflection (across a horizontal line)

7. Reflection (across a horizontal line) 8. Reflection (across a vertical line) 9. Reflection

(across a vertical line) 10. Rotation (3/4 turn clockwise; or turn counterclockwise)

Activity 2.6: Is the Shape Reflection-Congruent? 1. Give each student a geo-reflector and introduce the students to its parts. Place the geo-

reflector in front of the student so that the beveled edge is down (touching the desk) and the

beveled edge is facing the student.


2. Point to the parts of the geo-reflector as you describe them to the students. Say: This is a

geo-reflector. Feel the top edge of the geo-reflector. It has square corners for edges.

Feel the Bottom edge of the geo-reflector. Is it the same as the top edge? (No) Notice

that it is not as thick as any other edge on the geo-reflector. It has a beveled edge on the

front face of the geo-reflector and a square corner edge on the back face of the geo-

reflector. When you are working, always keep the beveled edge of the geo-reflector

facing you so that you are looking into the front face of the geo-reflector.

3. Then review the parts of the geo-reflector by asking:

a. How can you tell the top from the bottom? (The beveled edge is on the bottom.) b. How is the beveled edge different from all the other edges of the geo-reflector?

(It is a different thickness.) c. How can you tell which face is the front? (By finding the beveled edge that is on

the front face.)

4. Say: Now, go back to the bottom of Student Activity Sheet #6. Place the Geo-Reflector

on the line of reflection and rotate your book around so that the Geo-Reflector is sitting

horizontally, parallel to the table’s edge.

5. Say: Now take out a yellow pattern block and place it anywhere between you and the

Geo-Reflector. Using a pencil draw the perimeter of the yellow hexagon. Now, making

sure the hexagon stays in this same spot, look through the Geo-Reflector and what do

you see? (reflection of the hexagon) Yes, you see the reflection of the hexagon. Now I

would like you to draw the perimeter of the reflection of the hexagon free hand. Once

this is done, say: Remove the Geo-Reflector and pattern block leaving the drawing of the

original figure, the line of reflection, and the drawing of the figure’s reflection, called

the image of reflection.

6. Say: Now take out a few pattern blocks and place them in front of the Geo-Reflector

and look through the Geo-Reflector at their reflection.

7. Say: Now we are going to check to see whether two shapes are congruent as a result of a

reflection. Take out Lesson #13: Student Activity Sheet #8: Is the Shape Reflective-

Congruent. Place the Geo-Reflector between the two figures and move it around so

that when you look into the Geo-Reflector you can see whether the one figure fits on top

of the other. The figure between you and the Geo-Reflector, or what is in front of the

Geo-Reflector is called the “object.” Notice that the object is outlined in black. The

figure behind the Geo-Reflector is the “image.” What color is the image? (It is outlined

in the color of the Geo-Reflector as a result of looking through the colored plastic.)

8. If the object and the image are congruent (e.g. same size and same shape), the pair of

shapes are reflective-congruent. Use the Geo-Reflector to determine whether the other

pairs of figures are reflective-congruent. Check Yes if they are and No if they are not.

If they are congruent as a result of the reflection, draw the line of reflection by placing

your pencil on the beveled edge and drawing along that edge when the object reflects

onto the image.


Answers:

A.) Yes E). No

B.) No F.) Yes

C.) No G.) No

D.) Yes H.) Yes

Goal 3: Identify and Draw Lines of Symmetry

Activity 3.1: Lines of Symmetry 1. Ask students: What is a line of symmetry? (A line of symmetry divides a symmetrical

figure, object, or arrangement of objects into two parts that are congruent if one part is

reflected (flipped) over the line of symmetry.) Symmetry is everywhere—in nature, art,

music, mathematics, and beyond. Can you think of anything that is symmetrical?

(Answers might include a butterfly, the letter H, a pair of pants, etc.)

2. In this activity, students will enhance their understanding of symmetry, particularly,

reflectional symmetry, using the Geo-Reflector. Say: In our last activity, when shapes were

congruent as a result of a reflection, we were able to draw a line of reflection. This line

represented the line across which the objects were flipped. In this activity we will use

the Geo-Reflector on individual shapes as a line of symmetry. The reflection will

produce the other congruent half of the shape. Consequently, we will learn that a line

of symmetry is a line that divides a figure in to congruent halves, each of which is the

reflection image of the other.

3. Say: Take out Lesson #13: Student Activity Sheet #9: Line of Symmetry. The dotted

line on each shape is the line of symmetry. Place your Geo-Reflector on the dotted line and

draw the other side of the shape by tracing its reflection.

4. Answers: Line of Symmetry

Activity 3.2:

Polygons:

How Many Lines of Symmetry? 1. Say: Take out Lesson #13: Student Activity #10: Polygons: How Many Lines of

Symmetry? The polygons on this page are regular polygons. Regular polygons are

polygons that have congruent sides and congruent angles; that is sides of the same

lengths and angles of the same angle measure.

2. Say: You are going to determine how many lines of symmetry each of these polygons

has using the Geo-Reflector. Move your Geo-Reflector around on the shape to find


lines of symmetry. When you find a line of symmetry, where one side can be reflected

on the other, draw that line of symmetry by placing your pencil on the recessed

(beveled) edge of the Geo-Reflector and drawing that line. As you complete each

polygon, report the number of lines of symmetry for the identified shape in the table

below. Work on this activity now and then we will summarize your findings in the table

once you have finished.

Lines of Symmetry:

Triangle: 3 Square: 4 Pentagon: 5 Hexagon: 6

3. Say: Now, let’s review the data you have collected in the table. How many lines of

symmetry did you find for the equilateral triangle? (3) As you look back at these lines,

notice that each line went through one vertex and through the midpoint of the side

opposite the vertex. Now look at the five–sided pentagon. How many lines of symmetry

did you find for the pentagon? (5) How are these lines of symmetry similar to the lines

of symmetry in the triangle? (Each line of symmetry went through one vertex and through

the midpoint of the side opposite the vertex.)

4. Say: How many lines of symmetry did you find for the square? (4) As you look back

at these lines, notice that two line went from one vertex through to the other vertex, and

two line went from one midpoint through to the other midpoint on the opposite side.

Now look at the six–sided hexagon. How many lines of symmetry did you find for the

hexagon? (6) How are these lines of symmetry similar in the hexagon similar to the

lines of symmetry in the square? (Each line of symmetry went from one vertex to the

opposite vertex, or from one midpoint to the opposite the midpoint.)

5. Say: Now, let’s look at the numbers. Is there any relationship between the number of

sides in a regular polygon and the number of lines of symmetry? (Yes, when finding lines

of symmetry in regular polygons, the number of lines of symmetry equals the number of sides

in the polygon.)

Lesson #13: Assessment of Student Learning 1. Have students complete the thirteen multiple-choice assessment items independently by

circling the correct answer.

2. Once complete, discuss the items that the students answered incorrectly, asking them to

explain their thinking and reasoning about how they chose each answer.

Answer Key:

1. B 2. C 3. A 4. C 5. B 6. A 7. C 8. B 9. C 10. J

11. G 12. A 13. J


Lesson #13: Student Activity Sheet #1

Congruent or Not?

Look at these figures and see if you can pick congruent figures.

Check yes if the figures are congruent and no if the figures are not congruent.

Congruent or Not? Yes No Congruent or Not? Yes No

1.

9.

2.

10.

3.

11.

4.

12.

5.

13.

6.

14.

7.

15.

8.

16.



Tantalizing Triangles

Find out if the tantalizing triangles are congruent using tracing paper. Color any

congruent triangles you find the same color. Hint: There are four congruent shapes

for each of four different shapes!

A

B

C

D E

F

G

J

H

I

L

N

O

K P

M

Four Congruent Triangles are:_______________ Four Congruent Triangles are:_______________

Four Congruent Triangles are:_______________ Four Congruent Triangles are:_______________


Lesson #13: Student Activity Sheet #3A Tangram Puzzles


Lesson #13: Student Activity Sheet #3B

Tangram Puzzles



Translation With Pattern Blocks

Translation "slides" an object a fixed distance in a given

direction. The original object (A) and its translation (A’)

have the same shape and size, and they face in the same direction.

Part A: Translate the pattern blocks the distance and the direction indicated

by the arrows and draw the image of the translation.

Part B: Check yes or no to indicate whether one figure is a translation of the other.

Translation or Not? Yes No Translation or Not? Yes No

1.

3.

2.

4.



Discover Rotation

Check the yes or no box to indicate whether one figure is a rotation of another.

Rotation or Not? Yes No Rotation or Not? Yes No

1.

3.

2.

4.

Center

Center of

Rotation

Rotation

B

One-Fourth Turn or

Rotation of 90o



Rotation and Reflection With Pattern Blocks

Part A: Math Buddy A makes a pattern block figure on line A. Math Buddy B

makes the one-quarter rotation of Math Buddy A’s pattern block figures on line B.

Part B: Math Buddy A makes a pattern block figure on one side of the line. Math

Buddy B makes its reflection on the other side of the line.

Line B

Lin

e A

Center of

Rotation

Line of Reflection



Rotation or Reflection?

Check The Correct Transformation(s): Rotation Reflection



Is the Shape Reflective-Congruent?

Use your Geo-Reflector to check if the shapes are congruent as a result of a

reflection. Check “Yes” if they are and draw the line of reflection; otherwise

check “No.”

A. _____Yes _____No E. _____Yes _____No

B. _____Yes _____No F. _____Yes _____No

C. _____Yes _____No G. _____Yes _____No

D. _____Yes _____No H. _____Yes _____No



Line Of Symmetry Using the Geo-Reflector



Polygons: How Many Lines of Symmetry? Use the Geo-Reflector to draw as many lines of symmetry as you can find for each

“regular” polygon. Complete the chart identifying the number of lines of symmetry.

Shape Name of Shape Number of

Sides

Number of Lines of

Symmetry

Triangle

(Equilateral Triangle)

3

Square 4

Pentagon

(Regular Pentagon)

5

Hexagon

(Regular Hexagon)

6


Lesson #13:

Student Assessments

1. The arrow below moved 90 degrees

clockwise or turn.

This is an example of what?

A. Translation

B. Rotation

C. Reflection

2. The example below is a

demonstration of a __________.

A. Translation

B. Rotation

C. Reflection

3. The change in the position of the

triangles in Set A to the position of

the triangles in Set B is an illustration

of a __________.

A. Translation

B. Rotation

C. Reflection


demonstration of what?

A. Translation

B. Rotation

C. Reflection

5. In the example below, the triangles

going from left to right is an

illustration of a _____________.

A. Translation

B. Rotation

C. Reflection

6. What is it called when the arrow in

picture A is moved up to the position

in picture B?

A. Translation

B. Rotation

C. Reflection

Set A Set B

Picture A Picture B


7. The arrow below in picture B is a

mirror image of the arrow in picture

A. This transformation is called a

__________.

A. Translation

B. Rotation

C. Reflection


demonstration of a __________.

A. Translation

B. Rotation

C. Reflection

9. In which figure below is the line NOT

a line of symmetry?

Figure A Figure B Figure C

A. Figure A

B. Figure B

C. Figure C

10.

11. Which pair of figures does NOT show

a translation?

Picture A Picture B


12.

13.


Lesson #13: Teacher Sheet #1

Transformations: Translations, Rotations and Reflections

Translation: To translate an object means to move it a given distance in a

given direction without rotating or reflecting it.

Rotation To rotate an object means to turn it around. Every rotation has a

center of rotation and an angle of rotation. 90o angle is of a turn.

Reflection To reflect an object means to flip it to produce its mirror image.

Every reflection has a line of reflection along which it is flipped.

Translation

Slides a given

distance in a given

direction

Rotation

Turns around a center

point of rotation, for a

given angle or identified

turn (example of turn )

reflection

Flips across a line of

reflection

Math Buddies – Grade 4

13-27

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Lesson #13 Congruence, Symmetry and …acpssharepoint.appomattox.k12.va.us/AMS/amsteams/amsencore...Transformations: Translations, Reflections, and Rotations ... creates an image from