Table of Contents Date Topic Page(s) 9/14/15 Table of Contents (TOC) 1 3 9/14/15 Notebook Rubric 4 9/14/15 Unit A Reference Sheets 5 6

Transcription

1 Table of Contents Date Topic Page(s) 9/14/15 Table of Contents (TOC) 1 3 9/14/15 Notebook Rubric 4 9/14/15 Unit A Reference Sheets 5 6 9/14/15 September Calendar 7 9/14/15 Class Notes Template 8 9/15/15 Transformation Intro 9a 9e 9/15/15 Transformation Intro HW 10 9/22/15 Rotations 9/22/15 Reflections 11a 11? 12a 12? 1

2 Isometry Superimpose When transforming a figure in a plane. If the image is congruent to the preimage, then the transformation is a congruence transformation, or an isometry. place or lay (one thing) over another, typically so that both are still evident. ***to superimpose is the same as to map*** 2

3 Obj:Students manipulate rotations by each parameter: center of rotation, angle of rotation. Unit Circle in degrees 8/22/15 Start at 0 0 End at Origin Origin The origin is a center of rotation for rotation transformations. Rotation denoted as R (center, degrees) Ex. Rotation by 270 about the origin: R(origin, 270 ) Coordinate 90 CCW 180 CCW 270 CCW R1(origin, 90)(Poly) = Poly' R2(origin, 90)(Poly') = Poly'' = R1(origin, 180)(Poly) R3(origin, 90)(Poly'') = Poly''' = R1(origin, 270)(Poly) ( y,x) ( x, y) (y, x) examples of equivalent transformations Rotational Symmetry An object has rotational symmetry if there is a center point around which the object is rotated a certain number of degrees and the object looks the same. The number of positions in which the object looks exactly the same is called the order of the symmetry. yes, 5 order of symmetries yes, 3 order of symmetries Identity Symmetry A symmetry of a figure is a basic rigid motion that maps the figure back into itself. This is referred as the "do nothing" symmetry. a rotation by is equivalent to doing nothing, i.e., the identity transformation! 3

4 Obj: Students learn the precise definition of a reflection and construct the line of reflection of a figure and it's reflected image. Lines of reflection y axis 8/22/15 x axis Reflection denoted as R (line of reflection) Ex. Reflection across the y axis: R(y axis) Coordinate x axis (x, y) y axis ( x,y) Line y=x (y,x) Line y= x ( y, x) Composition of functions Reflection over parallel lines theorem "Function Composition" is applying one function to the results of another: The result of f() is sent through g() it is written: do last which means: do first do first the output of the first function is the input of the last function. If you compose two reflections do last over parallel lines that are h units apart, it is the same as a single translation of 2h units. *reflections over parallel lines is a single translation. translation of 16 units down Reflection over the Axes Theorem: If you compose two reflections over each axis, then the final image is a rotation of 180 of the original. Ry axis(rx axis( )) = R(F, 180)( ) Reflection over If you compose two reflections over lines that intersect at x, Intersecting Lines then the resulting image is a rotation of 2x, where the center of Theorem: rotation is the point of intersection. ex Rx axis(ry=x(abcd)) Reflection If you can reflect a figure over a line and the figure Symmetry appears unchanged, then the figure has reflection symmetry or line symmetry. The line that you reflect over is called the line of symmetry. A line of symmetry divides a figure into two mirror image halves. 4

5 End of Lesson Quiz Decide whether each of the statements is true or false. Provide a counterexample if the answer is false. a. If a figure has exactly two lines of symmetry, it has exactly two rotational symmetries (including the identity symmetry). b. If a figure has at least three lines of symmetry, it has at least three rotational symmetries (including the identity symmetry). c. If a figure has exactly two rotational symmetries (including the identity symmetry), it has exactly two lines of symmetry. d. If a figure has at least three rotational symmetries (including the identity symmetry), it has at least three lines of symmetry. 5