Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Geometry
Period:________ Date:_________
Module 1 – Topic C – Lesson 14 – Reflections
The purpose of lesson 14 is for students to identify the properties of reflection, to use constructions to find
line of reflection, get familiar with notations for reflections and express on their own words the properties of
reflections
Do Now: It is important to review how to contruct the perpendicular bisector of a segment and the
perpendicular bisector that goes through an external point.
Finding the line of reflection : Instruction steps that are included on the classwork apply for all the lesson
Remember the steps for constructing the line of reflection…
1. Construct a segment connecting a point on the pre-image and the corresponding point on the image.
2. Construct the perpendicular bisector of that segment
Remember the steps for reflecting…
1.
Construct a line perpendicular to the line of reflection passing through any point on the given shape
G-CO.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
G-CO.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph
paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure
onto another.
G-CO.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string,
reflective devices, paper folding, dynamic geometric software, etc.
Focus Standards
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Lesson 14 – Reflections
Warm Up
1. Construct the perpendicular bisector of segment AB
2. Construct the perpendicular bisector of segment CD that goes through an external point A
A
3. A rotation is shown below. If the dark P is the preimage and the light P is the image, state the angle of
rotation and give the correct notation for this transformation.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Lesson 14 – Reflections
Learning Targets :
 I can construct the line of reflection using the compass and a straightedge
 I can draw the reflected figure using a compass and a straightedge
 I can expres the properties of reflections in my own words
Example 1 (Discussion)
∆𝐴𝐵𝐶 is reflected across DE and maps onto ∆𝐴′𝐵′𝐶′.
Use your compass and straightedge to construct the perpendicular bisector of the segment connecting
𝐴 to 𝐴′.
What do you notice about the perpendicular bisector?
Label the point of intersection of DE and AA' as point P. What’s true about AP and A’P?
Example 2
a) Using the diagram to the right, construct the line of
reflection for quadrilaterals ABCD and A’B’C’D’.
Label the line of reflection XY .
b) If it was known that BC = 5, what is B’C’?
c) If it was known that mABC = 70o, find mA’B’C’.
d) What type of angle is formed by XY and BB ' ?
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________

In Conclusion……
So, we just learned that the line of reflection is the _________________ ___________________ of the
segment connecting a point on the pre-image and the corresponding point on the image.

We also learned that the distance between a point on the pre-image and the line of reflection is
___________ to the distance between a point on the image and the line of reflection.

In other words, a point on the pre-image and its corresponding point on the image are
_________________________ from the line of reflection.
𝒓𝒍
Notation:
𝒓𝒍 (𝑷) = 𝑸
Two Basic Properties of Reflections:
1. For any point 𝑃 on the line 𝑙,
𝑟𝑙 (𝑃) = 𝑃.
2. For any point 𝑃 not on 𝑙, 𝑟𝑙 (𝑃) is the point 𝑄 so that 𝑙 is the perpendicular bisector of the segment 𝑃𝑄.
Quick Write
Rewrite these two properties in your own words below:
1.
2.
Example 3
Construct the line of reflection for the pair of images at right.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Reflecting an image over a line of reflection
Example 4. Steps to creating the image of a reflection.
1. Construct a line perpendicular to OE passing through A.
2. Using your compass, measure the distance from A to OE along the perpendicular bisector.
3. Using that measurement on your compass, make an arc by putting the tip of your compass on the
point of intersection of the perpendicular bisector and OE and drawing an arc that intersects the
perpendicular bisector below OE .
4. Label the new point A’.
5. Repeat this process for all remaining points.
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
Lesson 14 – Reflections
Classwork
Exercise 1. Construct the line of reflection for the
image below.
Remember the steps for constructing the line of
reflection…
1. Construct a segment connecting a point on the
pre-image and the corresponding point on the
image.
2. Construct the perpendicular bisector of that
segment
Remember the steps for reflecting…
Exercise 2. Reflect ABCD across line segment EF .
1.
Construct a line perpendicular to EF
passing through any point of the shape
Lesson 14
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
GEOMETRY
Name:___________________________________
Period:________ Date:_________
For Exercises 3 and 4, construct the line of reflection for each pair of figures.
3)
4)
Remember the steps for reflecting…
For exercises 5 –7 , reflect the figure across the line provided.
5)
1. 1. Construct a line perpendicular to EF
passing through any point of the shape
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14
M1
GEOMETRY
Name:___________________________________
6)
7)
Period:________ Date:_________