1. Five-Minute Check (over Lesson 1–6) Mathematical Practices Then/Now
New Vocabulary
Key Concept: Reflections, Translations, and Rotations
Example 1: Identify Rigid Transformations
Example 2: Real-World Example: Estimate a Zero by Graphing
Example 3: Reflections on the Coordinate Plane
Lesson Menu

2. Name two congruent segments if 1  2.B. C. D.
5-Minute Check 1

3. A. R  W
B. S  V
C. S  U
D. S  T
5-Minute Check 2

4. Find mR if mRUV = 65.
A. 30
B. 40
C. 50
D. 60
5-Minute Check 3

5. Find mC if ΔABC is isosceles with AB  AC and mA = 70.
___
A. 45
B. 55
C. 70
D. 110
5-Minute Check 4

6. Find x if ΔLMN is equilateral with LM = 2x – 4, MN = x + 6, and LN = 3x – 14.
B. 10
C. 5
D. 2
5-Minute Check 5

7. D. no sides are congruent
In isosceles triangle BCD, C is the vertex angle. Which sides are congruent?
A. BC  CD
B. BC  BD
C. BD  CD
D. no sides are congruent
5-Minute Check 6

8. Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
Content Standards
G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). MP

9. You proved whether two triangles were congruent.
Identify reflections, translations, and rotations.
Verify congruence after a congruence transformation.
Then/Now

10. transformation preimage Image rigid transformation isometry reflection
translation
translation vector
rotation
Vocabulary

11. Concept

12. Answer: This is a translation.
Identify Rigid Transformations
A. Identify the type of rigid 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

13. Answer: This is a rotation.
Identify Rigid Transformations
B. Identify the type of rigid 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

14. Each vertex and its image are the same distance from the x-axis.
Identify Rigid Transformations
C. Identify the type of rigid 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 in the x-axis.
Example 1

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

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

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. BRIDGES Refer to the picture below. Identify the
Identify a Real-World Transformation
BRIDGES Refer to the picture below. Identify the
type of rigid 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

19. 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

20. Reflection in the x-axis.
Reflections on the Coordinate Plane
Consider △PSR that has coordinates P(−3, 4), S(−3, −1), and R(−6, 2). Determine the coordinates of the vertices of the image after a reflection in the x-axis.
Reflection in the x-axis.
Answer: P′ (−3, -4), S′(−3, 1), and R′(−6, −2)
Example 3

21. 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

22. Answer: A′(−3, 3), B′(−2, 6), C′ (2, 3), and D′(3, 6)
Translations on the Coordinate Plane
For parallelogram ABCD with vertices A(−2, 1), B(−1, 4), C(3, 1), and D(4, 4), find the coordinates of the vertices of the image after a translation along the vector
Translating along moves the figure 1 unit to the left and 2 units up.
Answer: A′(−3, 3), B′(−2, 6), C′ (2, 3), and D′(3, 6)