Warm Up Write a conjecture of what is going on in the picture

UNIT 2 Segment1:Transformation Lesson:2.1 Reflection Essential Question: Explain How isometry correlates with reflection Lesson 10-5: Transformations

Isometry AKA: congruence transformation a transformation in which an original figure and its image are congruent.

Types of Transformations Reflections: These are like mirror images as seen across a line or a point. Translations ( or slides): This moves the figure to a new location with no change to the looks of the figure. Rotations: This turns the figure clockwise or counter-clockwise but doesn’t change the figure. Dilations: This reduces or enlarges the figure to a similar figure. Lesson 10-5: Transformations

Pre-Image:original figure Image:after transformation. Use prime notation Notation: A A’ B B’ C C ’

Reflections You could fold the picture along line l and the left figure would coincide with the corresponding parts of right figure. Lesson 10-5: Transformations l You can reflect a figure using a line or a point. All measures (lines and angles) are preserved but in a mirror image. Example:The figure is reflected across line l.

Properties of reflections PRESERVE Size (area, length, perimeter…) Shape CHANGE orientation (flipped)

Reflect x-axis: (a, b) -> (a,-b) Change sign y-coordinate

Reflect y-axis: (a, b) -> (-a, b) Change sign on x coordinate

Reflections – continued… reflects across the y axis to line n (2, 1)  (-2, 1) & (5, 4)  (-5, 4) Lesson 10-5: Transformations Reflection across the x-axis: the x values stay the same and the y values change sign. (x, y)  (x, -y) Reflection across the y-axis: the y values stay the same and the x values change sign. (x, y)  (-x, y) Example:In this figure, line l : reflects across the x axis to line m. (2, 1)  (2, -1) & (5, 4)  (5, -4) ln m

Reflections across specific lines: To reflect a figure across the line y = a or x = a, mark the corresponding points equidistant from the line. i.e. If a point is 2 units above the line its corresponding image point must be 2 points below the line. Lesson 10-5: Transformations (-3, 6)  (-3, -4) (-6, 2)  (-6, 0) (2, 3)  (2, -1). Example: Reflect the fig. across the line y = 1.

PARTNER SWAP: Part I: (Live under my rules) Use graphing paper to graph a triangle label 3 points Swap with your partner Have him reflect over y=x WRITE a conjecture about how (a, b) will be changed after reflecting over y = x. Explain. Repeat by reflecting over the line y = -x. Write a conjecture.

PARTNER SWAP: Part I: (Live under my rules) Use graphing paper to graph a triangle label 3 points Swap with your partner Have him reflect over y=x WRITE a conjecture about how (a, b) will be changed after reflecting over y = x. Explain. Repeat by reflecting over the line y = -x. Write a conjecture.

Homework Complete the Vocabulary Pg odd 24,25 and 26 Lesson 10-5: Transformations