Lesson Plan #40
Class: Geometry
Date: Wednesday December 14th, 2016
Topic: Reflections
Aim: How do we perform a line reflection?
Objectives:
1) Students will be able to perform line reflections.
2) Students will be able to perform point reflections.
l
Do Now:
Imagine that the linel is a mirror. Draw the mirror image of the curve on the other side of the line.
What technique did you use to draw the mirror image of the curve on the other side of the line?
What general name do we give to a change in the position, size or shape of a figure?
HW #40:
Page 580 #’s 9-14
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Assignment #1: Using half a sheet of legal paper holding it in the landscape position, fold the
paper in half and with a pen/pencil draw in the line in the fold. On the left side, using a
straight-edge, draw a scalene triangle. Fold the paper and trace the triangle on the back of the
right side then trace that one on the front of the right side. Label the left triangle ABC, and the
image on the right side A’B’C’. What can we say about the two triangles?
Why? ______________________________________________________________________
As a result, what can we say about the corresponding sides and angles?
Using a straight-edge, draw a line segment from A to A’.
What is the relationship between the line of reflection and line segment AA’?
Compare the orientation of the two triangles. _____________________________________
Online Activity:Let’s go to http://www.mathopenref.com/reflectpoint.html to examine a point being reflected through a line
Let’s go to http://nlvm.usu.edu/en/nav/frames_asid_298_g_4_t_3.html?open=activities&from=topic_t_3.html
Observations:
Transformations that preserve lengths of segments and measures of angles are called basic rigid motions.
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.
The line of reflection acts as the perpendicular bisector of each segment that joins a given point of the pre-image with the
respective point of the image.
Assignment #2:
Construct the segment that represents the line of reflection for
quadrilateral 𝐴𝐵𝐶𝐷 and its image 𝐴′𝐵′𝐶′𝐷′.
How did you construct the line of reflection?
What is true about each point on 𝐴𝐵𝐶𝐷 and its corresponding point on
𝐴′𝐵′𝐶′𝐷′?
Assignment #3:
Assignment #4: Now let’s reflect a figure via construction!
Construct the reflection of segment AB through line L
rL(A)= _____
rL(B)= _____
What is the pre-image? _________
What is the image? __________
Assignment #5:
Reflect triangle ABC through the line
Assignment #6:
Medial Summary:
A transformation 𝑭 of the plane is a function that assigns to each point 𝑷 of the plane a unique point (𝑷) in the plane.
Transformations that preserve lengths of segments and measures of angles are called basic rigid motions.
A line reflection is a kind of transformation.
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.
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.)
Sample Test Questions:
1)
2)
Assignment #7: 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 whenthe figure is its own image under
a reflection in a line. Such a line is called an axis of symmetry.
Assignment #8: Which of the following words have line symmetry. If such symmetry
exists, draw the line of symmetry.
Sample Test Questions:
1)
2)
Assignment #9:
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 reflectioncreates 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 # 10:
Does this card look the same if you turn it upside down?
What is point symmetry? _____________________________________________
Assignment #11:
Sample Test Questions:
1)
2)
3)
4)