1. Check to see if all three properties of a reflection are met. 1.
Example 1
Identify Reflections
Tell whether the red triangle is the reflection of the blue triangle in line m.
SOLUTION
Check to see if all three properties of a reflection are met. 1.
Is the image congruent to the original figure? Yes. 2.
Is the orientation of the image reversed? Yes.
∆FGH has a clockwise orientation.
∆F'G'H' has a counter clockwise orientation. 3.
Is m the perpendicular bisector of the segments connecting the corresponding points? Yes. 1

2. To check, draw a diagram and connect the corresponding endpoints.
Example 1
Identify Reflections
To check, draw a diagram and connect the corresponding endpoints.
Because all three properties are met, the red triangle is the reflection of the blue triangle in line m.
ANSWER 2

3. Check to see if all three properties of a reflection are met. SOLUTION
Example 2
Identify Reflections
Tell whether the red triangle is the reflection of the blue triangle in line m.
Check to see if all three properties of a reflection are met.
SOLUTION 1.
Is the image congruent to the original figure? Yes. 2.
Is the orientation of the image reversed? No.
The red triangle is not a reflection of the blue triangle.
ANSWER 3

4. Which segment is the reflection of AB in the x-axis? Which point
Example 3
Reflections in a Coordinate Plane
Which segment is the reflection
of AB in the x-axis? Which point
corresponds to A? to B? a. b.
Which segment is the reflection of AB in the y-axis? Which point corresponds to A? to B?
SOLUTION a.
The x-axis is the perpendicular bisector of AJ and BK, so the reflection of AB in the x-axis is JK.
A is reflected onto J.
A(–4, 1) J(–4, –1)
B is reflected onto K.
B(–1, 3) K(–1, –3) 4

5. Example 3
Reflections in a Coordinate Plane
Which segment is the reflection of AB in the y-axis? Which point corresponds to A? to B? b.
The y-axis is the perpendicular bisector of AD and BE, so the reflection of AB in the y-axis is DE.
A is reflected onto D.
A(–4, 1) D(4, 1)
B is reflected onto E.
B(–1, 3) E(1, 3) 5

6. Checkpoint
Identify Reflections
Tell whether the red figure is a reflection of the blue figure. If the red figure is a reflection, name the line of reflection. 1. 2. 3.
ANSWER
yes; the x-axis
ANSWER no
ANSWER
yes; the y-axis