Name: Geometry Pd. Unit 1: Rigid Motions and Congruency 1-1 Rigid Motions and transformations o Rigid Motions produce congruent figures. o Translation, Rotation, Reflections are all rigid motions o Rigid Motions preserve size, shape and angle measure, they only change the position of a figure Unit 1 Review Date: 1-2 Translations o Ta,b o a how to move your pre-image left/right o b how to move your pre-image up/down o Vectors are drawn from pre-image to image and show distance and direction of the slide. 1-3 Reflections Notation: r Steps: 1. Graph line of reflection 2. Count how far away each point is on the line and count the opposite going the other way 1-4 Special reflections o Point Reflections o YOU MUST MEMORIZE ry=x and ry=-x Switch coordinates Switch and negate coordinates 1-5 Special compositions o Perform Compositions from right to left! o Composition of reflections over parallel lines are the same as one translation o Composition of reflections over perpendicular lines are the same as one rotation 1-7 Rotations and more special compositions Notation: R o Either know your rules, or Rotate paper! o Rotate counterclockwise for positive angles, and clockwise for negative angles! o Composition of reflections over perpendicular lines are the same as one rotation 1-8 Rotational Symmetry Order (How many clicks in one full revolution) 360 to find least amount of degrees to map onto itself- Same formula to n fins one exterior angle 3 Transformations are Rigid Motions: YOU MUST CHECK THE ANSWER KEY. YOU MUST HAND THIS IN BEFORE YOU TAKE. YOUR TEST! Notation: Notation: Notation:
Station 1: 1-Step Rigid Motions Station 2: Compositions Station 3: Symmetry Station 4: Congruency Station 1: One Step Rigid Motions 1. What is the image of A(-4,0), B (-1,3), C(-4,3) under ry= - x? 3. Sketch a vector that demonstrates where the translation took place below and DESCRIBE the vector. 3. State the coordinates of the image of A(-2,0), B (-1,3), C(3,3) under ry= x? 4. Graph triangle ABC. A(1, 1), B(4, 5), C(3, 2) and reflect it through point (-2, 1). State the coordinates of the image! A(1, 1) B(4, 5) C(3, 2)
5. Graph segment RS with vertices R(4, 1) and S(6, 3) and its image after a 270 rotation about the origin. Show your work! 6. Using appropriate notation, state the rigid motion that is demonstrated below. Be specific. 7. Graph and state the coordinates of the image of A(0,0), B (3,0), C(3,3) under rx=3? Explain why some points kept their location or were invariant?
8. What type of transformation is shown below? What is the relationship between the pre-image segment and the image segment? Be specific! 9. Under what type of transformation, shown in the accompanying figure, is A B C the image of ABC? 10. Consider the following figure below. a) State the new location of point A (where does it land?) after a rotation of 270 counterclockwise around point O. b) State the new location of point D (where does it land?) after a rotation of 180 degrees counterclockwise around point O.
Station 2: Compositions 1. Consider the following composition: rx-axis T2,-3. Explain how you would perform this composition. (You may want to bullet/number your steps to be more organized)! 2. Describe a sequence of transformations that would map ABC onto DEF. 3. Below you can see a composition of reflections over lines that are parallel. This same transformation could have been done as one
4. a) Graph and state the coordinates of A B C, the image of ABC A(-1,1), B(-5,0) and C(-2,4) after the composition T 2,0 o R 180. Show your work! b) Complete the sentence: ABC and A B C are to each other. 5. a) State the composition of transformations shown right. (*Remember order matters*) b) Describe the single rigid motion that could have been performed instead of the composition:
Station 3: Symmetry 1. Consider the regular octagon below: a) Does the following figure have rotational symmetry? b) What is the least amount of degrees you must rotate the octagon so that it maps onto itself? c) What is the order of rotational symmetry of the polygon? 2. Sketch in the line (s) of symmetry for the following: a) b) State the order of rotational symmetry for the figure shown in part b, above. 3. Does the hubcap shown below have rotational symmetry? If yes, what is the order of the symmetry?
Station 4: Congruency 1. Sketch the reflection of triangle ABC in Line m and name it triangle A B C : Using rigid motions, explain why the two triangles are congruent. 2. The triangle in quadrant 1 was rotated 180 o to result its image in quadrant 3. (Shown below) Explain why the two triangles below are congruent. BE SPECIFIC!!!