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1.2 Transformations and Symmetry
Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. Warm-up (IN) 15 Minutes - The first part of the warm-up will be a review of the last lesson, and the 2nd is an algebra review to prepare the students for the algebra that will be done in the notes and homework with isosceles triangles. 20 minutes – Check answers to even problems from HW, then to over any questions.
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Notes Transformation – A change made to the size or shape of a figure
Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. Notes Transformation – A change made to the size or shape of a figure Image – The new figure, as a result of a transformation 41 minutes for notes Essential Questions: What is the isosceles triangle theorem and it’s converse?
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3 types of Transformations –
Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. 3 types of Transformations – Reflection – Flips a figure over a line Translation – Slides each point of a figure the same distance in the same direction Essential Questions: How can you use the Isosceles triangle theorem to write a paragraph proof?
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Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. Rotation – Every point of the figure moves along a circular path around a fixed point, called the center of rotation. Try a few! Are the following transformations reflections, rotations or translations?? Essential Questions: What are the median and altitude of a triangle?
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Reflection, Rotation, or Translation
1. Reflection, Rotation, or Translation Rotation
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Reflection, Rotation, or Translation
2. Reflection, Rotation, or Translation Translation
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Reflection, Rotation, or Translation
3. Reflection, Rotation, or Translation Reflection
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Reflection, Rotation, or Translation
4. Reflection, Rotation, or Translation Reflection
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Reflection, Rotation, or Translation
5. Reflection, Rotation, or Translation Rotation
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Reflection, Rotation, or Translation
6. Reflection, Rotation, or Translation Translation
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Reflection, Rotation, or Translation
7. Reflection, Rotation, or Translation Reflection
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Reflection, Rotation, or Translation
8. Reflection, Rotation, or Translation Translation
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Reflection, Rotation, or Translation
9. Reflection, Rotation, or Translation Rotation
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Why is this not perfect reflection?
10. Why is this not perfect reflection? The zebras have slightly different striping. One has its nose closer to the ground.
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Reflection, Rotation, or Translation
11. Reflection, Rotation, or Translation Reflection is probably the best answer because the inside part of the bird’s foot is slightly shorter than the outside part. However, this example from nature does not really fit exactly in any of the categories.
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Reflection, Rotation, or Translation
12. Reflection, Rotation, or Translation Translation.
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Reflection, Rotation, or Translation
13. Reflection, Rotation, or Translation Reflection. However, rotation of 180o will be the same.
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Reflection, Rotation, or Translation
14. Reflection, Rotation, or Translation Rotation
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Reflection, Rotation, or Translation
15. Reflection, Rotation, or Translation Reflection in several directions.
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Reflection, Rotation, or Translation
16. Reflection, Rotation, or Translation Rotation
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Reflection, Rotation, or Translation
17. Reflection, Rotation, or Translation Reflection. Note the position of the purple tips; rotation of 180o would cause the top purple tip to be on the bottom.
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Reflection, Rotation, or Translation
18. Reflection, Rotation, or Translation Translation.
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Reflection, Rotation, or Translation
19. Reflection in multiple mirrors.
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Reflection, Rotation, or Translation
20. Reflection, Rotation, or Translation Translation. Watch the colors.
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Reflection, Rotation, or Translation
21. Reflection, Rotation, or Translation Reflection. Note the position of the red parts.
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Reflection, Rotation, or Translation
22. Reflection, Rotation, or Translation Rotation. Note the red parts.
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Ex 1 – Perform each operation to the shape.
Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. Ex 1 – Perform each operation to the shape. a. Reflect it over the line Essential Questions: How are the median, altitude and angle bisector related in an isosceles triangle?
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b. Rotate it clockwise 90º about the point
Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. b. Rotate it clockwise 90º about the point c. Translate it to the right
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Triangle shifted down 6 units and the y-coor. decreased by 6!
Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. Ex 2 – How do the coordinates of the points on a triangle change when you translate the triangle down?. A(0,1), B(5,1), C(0,4) “A prime” - image A’( 0,-5) B’( 5,-5) C’( 0,-2) Triangle shifted down 6 units and the y-coor. decreased by 6! What about if you shifted it up? Left and right?
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Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. A figure has symmetry if the figure and its image coincide after a transformation. Symmetry – 3 types of Symmetry – Reflectional – Rotational –
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Ex 3 – Describe each objects symmetry.
Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. Translational – Ex 3 – Describe each objects symmetry. a. Rotational and reflectional
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Translational and reflectional
Learning Objective: To identify and perform transformations and to describe movement and patterns in real life situations. b. Translational and reflectional
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POW!! HW – you’ll find out next class!
Out – How can you tell whether a figure has symmetry? Summary – I see things with symmetry all the time, such as… POW!! HW – you’ll find out next class! 5 minutes for Summary and closing questions. I will have the students do the Out as a ticket out.
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