Geometry Unit 4 Note Sheets Date Name of Lesson. Tangrams Activity. Rigid Motions. Translations. Symmetry. Quiz. Reflections.

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1 Date Name of Lesson Tangrams Activity Rigid Motions Translations Symmetry Quiz Reflections Rotations Transformations Poster Activity Transformations Poster Activity Review of Transformations Composition of Transformations Review of Composition of Transformations Practice Test Unit Test 1

2 Tangrams Activity Vocabulary A translation is a transformation that slides a figure across a plane or through space. With translation all points of a figure move the same distance and the same direction. A rotation is a transformation that turns a figure about (around) a point or a line. Basically, rotation means to spin a shape. The point a figure turns around is called the center of rotation. The center of rotation can be on or outside the shape. A reflection is a transformation that flips a figure across a line. 2

3 Rigid Motions Notes Vocabulary: Transformation Preimage Image There are three different types of Transformations that we will be discussing in this Unit. Translation Transformation Example Reflection Rotation Identify the type of transformation shown

4 Vocabulary Isometry Which of the following transformations appear to be isometries? Triangle XZY with vertices X(2, 8), Z(6. 7) and Y(4, 2) is a transformation of ABC with vertices A(2, 8), B(6, 7) and C(4, 2). Graph the original figure and its transformation. Identify the transformation and verify that it is a congruence transformation. 4

5 Translations Notes Recall Definition Translation 1. Graph the triangle EFG with vertices E( 7, 1), F( 4, 4) and G( 3, 1). Then translate it 2 units right and 5 units up. Then write the coordinates of the image. E F G 2. Graph the triangle ABC with vertices A(2, 6), B(1, 1) and C(7, 5). Then translate it 4 units left and 1 units down. Then write the coordinates of the image. A B C Are there rules that we can write for these translations? 5

6 3. Graph the triangle TUV with vertices T( 1, 4), U(6, 2) and V(5, 5). Then translate it using the rule (x 3, y + 2). Then write the coordinates of the image. T U V You Turn 4. Graph the triangle PET with vertices P(1, 0), E(2, 2) and T(4, 1). Then translate it using the rule (x 5, y 1). Then write the coordinates of the image. P E T 6

7 Lines of Symmetry Symmetry Notes 7

8 Reflections Notes Triangle JKL has vertices J(0, 3), K( 2, 1), and L( 6, 1). Graph JKL and its image on the given line. 1. x = 4 2. y = 3 8

9 3. Graph ABC with vertices A( 5, 3), B(2, 0), and C 1, 2 and then reflect it over the x-axis. Then write the image s ordered pairs. 4. Graph ABC with vertices A(1, 1), B(3, 2), and C 4, 1 and then reflect it over the x-axis. Then write the image s ordered pairs. A A B B C C 3. Graph PQR with vertices P( 4, 1), Q(2, 3), and R 2, 1 and then reflect it over the y-axis. Then write the image s ordered pairs. 3. Graph ABC with vertices A(1, 1), B(3, 2), and C 4, 1 and then reflect it over the y-axis. Then write the image s ordered pairs. P A Q B R C Can we write a rule for reflecting over the x-axis? Can we write a rule for reflecting over the y-axis? 9

10 Rotations Notes Recall Definition Rotations 1. Triangle PQR has vertices P(1, 1), Q(4, 5), and R(5, 1). Graph PQR and its image after a rotation 90 about the origin. Then write the image s ordered pairs. P Q R 10

11 2. Triangle FGH has vertices F(2, 1), G(7, 1), and H(6, 3). Graph FGH and its image after a rotation 90 about the origin. Then write the image s ordered pairs. F G H Is there a rule we could write for rotation 90 about the origin? 3. Triangle DEF has vertices D( 2, 1), E( 1, 1), and F(1, 1). Graph FGH and its image after a rotation 180 about the origin. Then write the image s ordered pairs. D E F 11

12 4. Triangle ABC has vertices A(2, 2), B(3, 4), and C(6, 2). Graph ABC and its image after a rotation 180 about the origin. Then write the image s ordered pairs. A B C Is there a rule we could write for rotation 180 about the origin? 5. Triangle WXY has vertices W( 6, 3), X( 2, 3), and Y(1, 1). Graph WXY and its image after a rotation 270 about the origin. Then write the image s ordered pairs. W X Y 12

13 6. Triangle JKL has vertices J(3, 7), K(1, 1), and L(5, 3). Graph JKL and its image after a rotation 270 about the origin. Then write the image s ordered pairs. J K L Is there a rule we could write for rotation 270 about the origin? 7. Triangle DFG has vertices D( 2, 6), F(2, 8), and G(2, 3). Graph DFG and its image after a rotation clockwise 90 about the origin. Then write the image s ordered pairs. D F G 13

14 Transformations Poster Instructions Purpose: The activity will allow students to demonstrate their understanding of the coordinate system and apply their knowledge to various geometry concepts. This activity will enable students to apply, evaluate and create a product demonstrating their understanding of geometric transformations. Supplies: 4 sheets of graph paper 1 sheet of notebook paper 1 poster sheet or poster board Ruler Markers Procedure: Students will work in groups of three as decided by the teacher (NO ONE IS ALLOWED TO WORK ALONE). Group will complete a total of three transformations from their original figure. The original figure must contain a minimum of five points, and the points must be labeled alphabetically. Each transformation must be shown graphically, and the coordinates must be displayed. There must be a translation, reflection and rotation. The group must write a rule for each transformation, and identify which quadrants the transformed image is in. There must be a figure in at least three of the four quadrants after all the transformations are completed. Each graph must be drawn using a ruler and must be colored. Steps: 1. Place all four sheets of graph paper on the poster sheet and make a large coordinate grid (each paper should be one of the quadrants). 2. On the notebook paper you will make three columns: a. Original Point b. Transformation Rule c. Image Point 3. Complete each transformation (translation, reflection and rotation) 4. Color code each figure and label as original, translation, reflection and rotation. Groups will be given two class periods to complete this poster ( & ). If a group s poster is complete they can turn it in on Thursday, If a group does not complete the poster during the class period it is up to the group to determine a time to get together to turn it in no later than Wednesday, in class. Late posters will have their grade deducted by 50% and are not accepted beyond

15 Composition of Transformations Notes Composition of Transformations 1. Triangle JKL has vertices J(6, 1), K(10, 2), and L(5, 3). Graph JKL and its image after a translation of (x, y + 4) and a reflection over the y-axis. Write the ordered pair after each transformation. J K L J K L 2. Triangle POR has vertices P(1, 1), Q(2, 5), and R(4, 2). Graph PQR and its image after a translation of (x 3, y 3) and a reflection over the x-axis. Write the ordered pair after each transformation. P Q R P Q R 15

16 3. Triangle CDE has vertices C( 7, 1), D( 3, 2), and E( 4, 4). Graph CDE and its image after a reflection over the x-axis and a rotation of 90 about the origin. Write the ordered pair after each transformation. C D E C D E 4. Triangle TUV has vertices T(2, 1), U(5, 2), and V(3, 4). Graph TUV and its image after 180 rotation and a reflection over y = 2. Write the ordered pair after each transformation. T U V T U V 16