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Geometry: Transformations & Congruence Mastery

Delve into reflections, translations, and rotations with practical examples and congruence verification after transformations. Improve your understanding of rigid motions and congruence with mathematical practices. Learn to identify different types of transformations such as reflections, translations, and rotations in real-world scenarios. Test your knowledge with quick checks and explore the principles of geometric transformations.

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Geometry: Transformations & Congruence Mastery

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 4–6) CCSS 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. A. B. C. D. Name two congruent segments if 1  2. 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. A. 20 B. 10 C. 5 D. 2 5-Minute Check 5

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

  9. 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

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

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

  12. Concept

  13. Identify Congruence Transformations A. Identify the type of congruence transformation shown as a reflection, translation, or rotation. Each vertex and its imageare in the same position, just5 units right and 2 units down. Answer: This is a translation. Example 1

  14. 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. 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. A. reflection 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. A. reflection 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. A. reflection 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. 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

  22. 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

  23. Verify Congruence after a Transformation Example 3

  24. Verify Congruence after a Transformation Answer:By SSS, ΔJKL ΔPQR. CheckUse 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. A. B. C. D. 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. Example 3

  26. End of the Lesson

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