1. Congruence Transformations
LESSON 4–7
Congruence Transformations

2. Five-Minute Check (over Lesson 4–6) TEKS Then/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

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

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

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

6. 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

7. 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

8. 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

9. Mathematical Processes G.1(A), G.1(D)
Targeted TEKS
G.6(C) Apply the definition of congruence, in terms of rigid
transformations, to identify congruent figures and their corresponding sides and angles.
Mathematical Processes
G.1(A), G.1(D)
TEKS

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

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

12. Concept

13. 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

14. 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

15. 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

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

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

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

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. 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.
Analyze You are asked to identify the type of transformation—reflection, translation, or rotation. Then, you need to show that the two figures are congruent.
Formulate Use the Distance Formula to find the measure of each side. Then show that the two triangles are congruent by SSS.
Example 3

22. Verify Congruence after a Transformation
Determine 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

23. Verify Congruence after a Transformation
Example 3

24. Answer: By SSS, ΔJKL  ΔPQR.
Verify Congruence after a Transformation
Answer: By SSS, ΔJKL  ΔPQR.
Justify Use the definition of a translation. Use a ruler to measure and compare the corresponding sides of the triangles. The corresponding sides are congruent, so the triangles are congruent.
Example 3

25. Evaluate By graphing the given information, we
Verify Congruence after a Transformation
Evaluate By graphing the given information, we
were able to visualize the problem. Visualization is an important problem solving tool. We then used known
formulas and definitions to determine the solution. The graph of the transformation appears to be a translation, so our answer is reasonable.
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

27. Congruence Transformations
LESSON 4–7
Congruence Transformations