Five-Minute Check (over Lesson 4–6) 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

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

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

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

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

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

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

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Lesson 4-7: Congruent Triangles (Pg.294) TARGETS Identify reflections, translations, and rotations. Verify congruence after a congruence transformation. Then/Now

Content Standards   G-CO.2 Represent transformation in the plane using, e.g., transparencies and geometry software; describe transformation as functions that take points in the plane as inputs and give other points as outputs. Compare transformation that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Mathematical Practices 2 Reason abstractly and quantitatively. 6 Attend to precision. Then/Now

Identify reflections, translations, and rotations. You proved whether two triangles were congruent. (Lessons 4–3, 4–4, and 4–5) Identify reflections, translations, and rotations. Verify congruence after a congruence transformation. Then/Now

congruence transformation preimage image isometry reflection translation rotation Vocabulary

Concept

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

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

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

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

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

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

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

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

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

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

Verify Congruence after a Transformation Example 3

Answer: By SSS, ΔJKL  ΔPQR. Verify Congruence after a Transformation Answer: By SSS, ΔJKL  ΔPQR. Check 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

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

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