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Lesson 11-1 Exit Ticket Similar Triangles Opening routine Unit 2: Similarity, Proof and Trigonometry Lesson 11 Similar Triangles Objective: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Essential Question: How do you use proportions to find side lengths of similar triangles? Lesson 11 Similar Triangles Vocabulary Proportion: Is the name that is given to a statement that two ratios are equal. In a proportion the cross products are equal. Similar triangles: Triangles are similar when they preserve angle measures. Similar triangles: Corresponding side lengths in similar triangles are proportional. Lesson 11 Similar Triangles Vocabulary Scale factor: Is the ratio between corresponding sides of similar triangles. Angle–Angle Similarity (AA) Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. Lesson 11 Similar Triangles Vocabulary Side–Side–Side Similarity (SSS) Theorem: If the corresponding side lengths of two triangles are proportional, then the triangles are similar. Side–Angle–Side Similarity (SAS) Theorem: If two sides of one triangle have lengths that are proportional to two sides of another triangle and the included angles of those sides are congruent, then the triangles are similar. Lesson 11 Similar Triangles Lesson 11 Similar Triangles Lesson 11 Similar Triangles Lesson 11 Similar Triangles Lesson 11 Similar Triangles Lesson 11 Similar Triangles Lesson 11 Similar Triangles Lesson 11 Similar Triangles Guided Practice – WE DO Lesson 11 Similar Triangles Independent Practice – YOU DO Row 1 Row 2 Row 3 Row 4 Row 5 Row 6 Question 1 page 94 Question 2 page 94 Question 1 page 94 Question 4 page 94 Question 5 page 94 Question 6 page 94 Lesson 11 Similar Triangles Independent Practice – YOU DO Lesson 11 Similar Triangles Independent Practice – YOU DO Lesson 11 Similar Triangles Independent Practice – YOU DO Lesson 11 Similar Triangles Re-teach MAFS.912.G-CO.1.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. 11. Rectangle STUV is graphed on the coordinate plane below. Which series of transformations carries rectangle STUV onto itself? Lesson 11 Similar Triangles 11. Rectangle STUV is graphed on the coordinate plane below. Which series of transformations carries rectangle STUV onto itself? A. reflection over the y-axis, rotation around the origin 180o clockwise, reflection over the y-axis False Lesson 11 Similar Triangles 11. Rectangle STUV is graphed on the coordinate plane below. Which series of transformations carries rectangle STUV onto itself? B. reflection over the x-axis, reflection over the y-axis, rotation around the origin 270o counterclockwise False Lesson 11 Similar Triangles 11. Rectangle STUV is graphed on the coordinate plane below. Which series of transformations carries rectangle STUV onto itself? C. reflection over the y-axis, reflection over the x-axis, rotation around the origin 180o counterclockwise True Lesson 11 Similar Triangles Re-teach MAFS.912.G-CO.2.6: 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. 8. Which sequence of rigid motions would move DEF so it completely covers D'E'F'? A. reflection of DEF across a vertical line followed by a translation to the right. False Lesson 11 Similar Triangles Re-teach MAFS.912.G-CO.2.6: 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. 8. Which sequence of rigid motions would move DEF so it completely covers D'E'F'? B. reflection of DEF across a vertical line followed by a translation down. False Lesson 11 Similar Triangles Re-teach MAFS.912.G-CO.2.6: 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. 8. Which sequence of rigid motions would move DEF so it completely covers D'E'F'? C. 90o clockwise rotation of DEF about the point E followed by a translation down. False Lesson 11 Similar Triangles Re-teach MAFS.912.G-CO.2.6: 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. 8. Which sequence of rigid motions would move DEF so it completely covers D'E'F'? D. 90o clockwise rotation of DEF about the point F followed by a translation to the right. True Lesson 11 Similar Triangles Closure Essential Question: How do you use proportions to find side lengths of similar triangles? Lesson 11 Similar Triangles Homework Geometric Constructions Packet Due Wednesday November 2, 2016