1. Key Concept: Reflections, Translations, and Rotations
CCSS
Now
New Vocabulary
Key Concept: Reflections, Translations, and Rotations
Example 1: Identify Congruence Transformations
Example 2: Real-World Example: Identify a Real-World Transformation
Example 3: Verify Congruence after a Transformation
Lesson Menu

2. Mathematical Practices
Content Standards
G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
7 Look for and make use of structure.
CCSS

3. SWBAT use mathematical vocabulary (key terms in geometry) IOT describe transformations in the coordinate plane.
SWBAT graph pre-images and images under reflection and rotation using a variety of tools IOT analyze the properties of transformations.
Then/Now

4. congruence transformation isometry reflection translation rotation
preimage
image
congruence transformation
isometry
reflection
translation
rotation
Vocabulary

5. Concept

6. Identify Congruence Transformations
A. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Each vertex and its image are in the same position, just 5 units right and 2 units down.
Answer:
Example 1

7. Answer: This is a translation.
Identify Congruence Transformations
A. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Each vertex and its image are in the same position, just 5 units right and 2 units down.
Answer: This is a translation.
Example 1

8. Identify Congruence Transformations
B. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Each vertex and its image are the same distance from the origin. The angles formed by each pair of corresponding points and the origin are congruent.
Answer:
Example 1

9. Answer: This is a rotation.
Identify Congruence Transformations
B. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Each vertex and its image are the same distance from the origin. The angles formed by each pair of corresponding points and the origin are congruent.
Answer: This is a rotation.
Example 1

10. Each vertex and its image are the same distance from the x-axis.
Identify Congruence Transformations
C. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Each vertex and its image are the same distance from the x-axis.
Answer:
Example 1

11. Each vertex and its image are the same distance from the x-axis.
Identify Congruence Transformations
C. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
Each vertex and its image are the same distance from the x-axis.
Answer: This is a reflection.
Example 1

12. A. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
B. translation
C. rotation
D. none of these
Example 1A

13. A. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
B. translation
C. rotation
D. none of these
Example 1A

14. B. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
B. translation
C. rotation
D. none of these
Example 1B

15. B. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
B. translation
C. rotation
D. none of these
Example 1B

16. C. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
B. translation
C. rotation
D. none of these
Example 1C

17. C. Identify the type of congruence transformation shown as a reflection, translation, or rotation.
B. translation
C. rotation
D. none of these
Example 1C

18. Identify a Real-World Transformation
BRIDGES Identify the type of congruence transformation shown by the image of the bridge in the river as a reflection, translation, or rotation.
Answer:
Example 2

19. Identify a Real-World Transformation
BRIDGES Identify the type of congruence transformation shown by the image of the bridge in the river as a reflection, translation, or rotation.
Answer: The image is a reflection, with the line at which the bridge meets the water as the line of reflection.
Example 2

20. GAME Identify the type of congruence transformation shown by the image of the chess piece as a reflection, translation, or rotation.
A. reflection
B. translation
C. rotation
D. none of these
Example 2

21. GAME Identify the type of congruence transformation shown by the image of the chess piece as a reflection, translation, or rotation.
A. reflection
B. translation
C. rotation
D. none of these
Example 2

22. Verify Congruence after a Transformation
Triangle PQR with vertices P(4, 2), Q(3, –3), and R(5, –2) is a transformation of ΔJKL with vertices J(–2, 0), K(–3, –5), and L(–1, –4). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation.
Understand You are asked to identify the type of transformation—reflection, translation, or rotation. Then, you need to show that the two figures are congruent.
Plan Use the Distance Formula to find the measure of each side. Then show that the two triangles are congruent by SSS.
Example 3

23. Verify Congruence after a Transformation
Solve Graph each figure. The transformation appears to be a translation 6 units right and 2 units up. Find the measures of the sides of each triangle.
Example 3

24. Verify Congruence after a Transformation
Example 3

25. Triangle ABC with vertices A(–1, –4), B(–4, –1), and C(–1, –1) is a transformation of ΔXYZ with vertices X(–1, 4), Y(–4, 1), and Z(–1, 1). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation. A. B. C. D.
Example 3

26. Triangle ABC with vertices A(–1, –4), B(–4, –1), and C(–1, –1) is a transformation of ΔXYZ with vertices X(–1, 4), Y(–4, 1), and Z(–1, 1). Graph the original figure and its image. Identify the transformation and verify that it is a congruence transformation. A. B. C. D.
Example 3