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Lesson 4-7 Congruence Transformations 5-Minute Check on Lesson 4-6 Transparency 4-7 Refer to the figure. 1. Name two congruent segments if 1 2. 2. Name two congruent angles if RS RT. 3. Find mR if mRUV = 65. 4. Find mC if ABC is isosceles with AB AC and mA = 70. 5. Find x if LMN is equilateral with LM = 2x – 4, MN = x + 6, and LN = 3x – 14. 6. Find the measures of the base angles of an isosceles triangle if the measure of the vertex angle is 58. Standardized Test Practice: A 32 B 58 C 61 D 122 5-Minute Check on Lesson 4-6 Transparency 4-7 Refer to the figure. 1. Name two congruent segments if 1 2. UW VW 2. Name two congruent angles if RS RT. S T 3. Find mR if mRUV = 65. 50 4. Find mC if ABC is isosceles with AB AC and mA = 70. 55 5. Find x if LMN is equilateral with LM = 2x – 4, MN = x + 6, and LN = 3x – 14. 10 6. Find the measures of the base angles of an isosceles triangle if the measure of the vertex angle is 58. Standardized Test Practice: A 32 B 58 C 61 D 122 Objectives • Identify reflections, translations, and rotations • Verify congruence after a congruence transformation Vocabulary • Transformation – operations that map a figure into another figure • Preimage – a figure before it is moved • Image – a figure after it has been moved • Congruence transformation – a rigid transformation that main the figures size and shape • Isometry – a rigid transformation • Reflection – a flip, reflects the figure over a line of reflection • Translation – a slide, moves the figure up or down; left or right; or a combination of the two • Rotation – a turn, is a transformation about a fixed point called the center of rotation Key Concept Identify Congruence Transformations • 1A. 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. Identify Congruence Transformations • 1B. 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. Identify Congruence Transformations • 1C. 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. 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. Verify Congruence after 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. 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. Verify Congruence after 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. 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. Verify Congruence after Transformation • Verify that it is a congruence transformation. Plan Use the Distance Formula to find the measure of each side. Then show that the two triangles are congruent by SSS. Verify Congruence after Transformation • Verify that it is a congruence transformation. Answer: By SSS, ΔJKL ΔPQR. Summary & Homework • Summary: – In a congruence transformation, the position of the image may differ from the preimage, but the two figures remain congruent. – Flips, turns, and slides are congruence transformations • Homework: – pg 297-8: 7-12, 13-16