Lesson Plan #90

Class: Geometry Date: Thursday April 19th, 2012

To pic : Reflections Aim: How do we perform a line reflection?

Objectives: 1) How do we perform a line reflection?

Do Now:Imagine that the line y=x is a mirror. Draw the mirror image of the curve on the other side of the line y=x

What technique did you use to draw the mirror image of the curve on the other side of the line y=x?

HW #90:Page 580 #’s 9-14

PROCEDURE: Write the Aim and Do NowGet students working! Take attendance Give Back HWCollect HWGo over the Do Now

Assignment #1:Let’s go to http://www.mathopenref.com/reflectpoint.html to examine a point being reflected through a line

Assignment #2:Reflect segment AB through line L

rL(A)= _____

rL(B)= _____

What is the pre-image? _________

What is the image? __________

Assignment #3:Reflect triangle ABC through the line

Assignment #4: Can we draw a line through the picture below so that the figure is its own image under a reflection through the line. If so, draw that line.

Definition: Line symmetry occurs in a figure when the figure is its own image under a reflection in a line. Such a line is called an axis of symmetry.

Assignment #5: Which of the following words have line symmetry. If such symmetry exists, copy the word and draw the line of symmetry.

Medial Summary:

A reflection over a line k (notation rk) is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the

line.  Remember that a reflection is a flip.  Under a reflection, the figure does not change size.  

 The line of reflection is the perpendicular bisector of the segment joining every point and its image.

A line reflection creates a figure that is congruent to the original figure and is called an isometry (a transformation that preserves length).  Since naming (lettering) the figure in a reflection requires changing the order of the letters (such as from clockwise to counterclockwise), a reflection is more specifically called a non-direct or opposite isometry. Properties preserved (invariant) under a line reflection:1.  distance (lengths of segments are the same)2.  angle measures (remain the same)3.  parallelism (parallel lines remain parallel)4.  collinearity (points stay on the same lines)5.  midpoint (midpoints remain the same in each figure)------------------------------------------------------------------6.  orientation (lettering order NOT preserved.  Order is reversed.)

Assignment #6: Let’s go to http://www.mathwarehouse.com/transformations/reflections-in-math.php to examine line reflections in the coordinate plane

Assignment #7:

Assignment #8: Sketch the graph of triangle ABC with vertices A(1,1), B(2,3)And C(4,2). Reflect the triangle through the origin. Reflect the triangle through the point (0,0), the origin. ( )

What kind of reflections is this known as?

A point reflection exists when a figure is built around a single point called the center of the figure, or point of reflection. For every point in the figure, there is another point found directly opposite it on the other side of the

center such that the point of reflection becomes the midpoint of the segment joining the point with its image. Under a point reflection, figures do not change size.

A point reflection creates a figure that is congruent to the original figure and is called an isometry (a transformation that preserves

length). Since the orientation in a point reflection remains the same (such as counterclockwise seen in this diagram), a point reflection is

more specifically called a direct isometry.

Properties preserved (invariant) under a point reflection:1. distance (lengths of segments are the same)2. angle measures (remain the same)3. parallelism (parallel lines remain parallel)

4. colinearity (points stay on the same lines)5. midpoint (midpoints remain the same in each figure)6. orientation (lettering order remains the same)Assignment #8:Determine if the playing card has point symmetry?

Assignment #9:

Assignment #10:

Assignment #11: