PROJECT Transformations Chapter 14 beginning on page 570 Student Notes

Project Grading Each page is worth 10 points unless noted otherwise. Total Project worth 200 points

Please take note! 1)This is a project for honors students. Research will need to be done! 2)Your work should be neat and organized. My advice is to use pencil. 3)Your work should contain original drawings. Please do not copy other students drawings! 4)Please use the correct spelling. 5)20 points will be deducted for every day this is late.

GOOD LUCK!

TRANSFORMATION or MAPPING: - a correspondence between points. Each point P in a given set is mapped to exactly one point P’ in the same or a different set. PREIMAGE: the original figure, P, in a transformation. IMAGE: the result, P’, of applying a transformation to a preimage. A transformation maps a preimage onto an image.

MIRA - this geometric tool has the reflective quality of a mirror as well as a transparent quality. By placing the MIRA on any shape, you quickly see concepts of symmetry and congruence. It is also very helpful in studying transformational geometry, as reflections, translations, rotations, and glide reflections are shown easily.

REFLECTION A transformation in which a line of reflection acts like a mirror, reflecting points to their images, … also known as a ?. A reflecting line is the line over which a preimage is reflected, … it is also known as a line of reflection.

REFLECTION C B A ACTIVITY: Reflect ∆ABC over the line. Use a mira and label the final image.

C B A ∙ ∙ ∙ C’C’ B’B’ A’A’ REFLECTION ACTIVITY: Reflect ∆ABC over the line. Use a mira and label the final image.

C B A ∙ ∙ ∙ REFLECTION ACTIVITY: Reflect ∆ABC over the line. Use a mira and label the final image. C’C’ A’A’ B’B’

C B A REFLECTION ACTIVITY: Reflect ∆ABC over the line. Use a mira and label the final image. C’C’ A’A’ B’B’

COMPOSITE of MAPPINGS A transformation that combines two mappings.

TRANSLATION A transformation that slides or glides all points of the plane the same direction, … also known as a slide or a ?. A translation is the composite of two reflections over parallel lines.

C B A ACTIVITY: Translate ∆ABC, by reflecting ∆ABC over x, then over y. Use a mira and label the final image. TRANSLATION xy Be sure to show ALL your markings!

ROTATION The composite of two reflections over intersecting lines, … also known as a ?.

ROTATION C B A ACTIVITY: Rotate ∆ABC, by reflecting ∆ABC over s, then over t. Use a mira and label the final image. s t Be sure to show ALL your markings!

GLIDE REFLECTION The composite of a reflection and a translation parallel to the reflection line, … also known as a ?.

C B A ACTIVITY: Glide reflect ∆ABC, by reflecting ∆ABC over x, then over y, then over z. Use a mira and label the final image. xy Be sure to show ALL your markings! GLIDE REFLECTION z

ISOMETRY A transformation that maps every segment to a congruent segment, … also known as a congruence mapping (or transformation).

State the formal name and nickname for each isometry in the order each was given in this project. 1.reflection ………….____________ 2.translation ………..____________ 3.rotation ……………____________ 4.glide reflection …..____________

Every isometry preserves the following: 1.Area 2.Angle Measure 3.Betweenness 4.Collinearity 5.Distance

Fill in the blank. Use either reflection, translation, rotation, or glide reflection. FOLLOW THE DIRECTIONS!!! You can figure this out! Activity

SYMMETRY An IDENTITY TRANSFORMATION is the mapping that maps every point to itself. FOLLOW THE DIRECTIONS!!! Use your template and remember to draw ALL the lines of symmetry as dashed lines!

LINE SYMMETRY FOLLOW THE DIRECTIONS!!! Do NOT forget to circle the letters!

ROTATIONAL SYMMETRY FOLLOW THE DIRECTIONS!!! Do NOT forget to circle the letters!

POINT SYMMETRY FOLLOW THE DIRECTIONS!!! Do NOT forget to circle the letters!

SYMMETRY “quiz” FOLLOW THE DIRECTIONS!!! USE YOUR TEMPLATE! REMEMBER that you are drawing polygons!

???? JEOPARDY ANSWER ???? FOLLOW THE DIRECTIONS!!! Click on this for help!

PLANE SYMMETRY A figure in space has plane symmetry if there is a symmetry plane such that the reflection in the plane maps the figure onto itself … also called bilateral symmetry.

READ & FOLLOW THE DIRECTIONS!!! Use the book for help, BUT DO NOT USE THEIR PICTURES or THE SAME TYPE OF OBJECT!!! They must be unique! DO NOT COPY!!!

Activity State two (2) unique real objects that have plane symmetry. State the number of symmetry planes for each object. Tape a picture of this real object in the space provided. And here are some examples.

example real 3D object: Monarch Butterfly 1 symmetry plane

example real 3D object: Starfish 5 symmetry planes

TESSELLATIONS A pattern in which congruent copies of a figure completely fill the plane without any gaps or overlapping.

Activity Draw a tessellation that completely tessellates the “plane” below with a figure from your template. Shade or color so the fundamental regions of your basic figure is known. FOLLOW THE DIRECTIONS!!! This is worth 15 points. Be careful not to have gaps and overlaps!

Activity Completely tessellate the “plane” using one (1) figure from your template. Bonus possible for nice work with color! Completely tessellate the “plane” using two (2) figures from your template. Bonus possible for nice work with color!

Mr. Kline’s Bathroom Floor Be sure to include a diagram with labels. Write a complete logical explanation. Remember to include mathematical support!

READ & FOLLOW THE DIRECTIONS!!! This is worth 15 points. Click here for help! Here are some examples made by former geometry students. Activity

SIMILARITY MAPPING READ & FOLLOW THE DIRECTIONS!!! Be sure to use POLYGONS! A transformation that maps any figure to a similar figure.

DILATION Fill in the blanks!!! Be sure to draw the images! A transformation in which a figure increases or decreases its size, but remains similar to its preimage.

Four Color Map Theorem The theorem states that any map can be filled in with no more than four (4) colors in such a way that no two countries with common borders (segments) have the same color. Mathematicians have never been able to prove or disprove the “Four-Color Map Theorem.” Here is a U.S.A. map example.

4 Color Map Theorem Directions The designs can be filled in with only 4 colors. Use colored pencils to fill in the areas so that no two areas of LIKE color touch. Multiple solutions are possible. HINT: Use a pencil to lightly write the first letter of each color in an area to work out a solution. Note: I should NOT see these letters when you are finished. Here is an example.

(1)

(2)

(3)

(4) Bonus points if this is done with 2 colors!

~ FINAL ACTIVITY ~ This is your final piece of work! Make it very nice!!! This is worth 20 points. REMEMBER: Completely fill the space! Add color! Here are some examples made by former geometry students.