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Module 2 Why Move Things Around Activating Prior Knowledge β What are rigid motion transformations? Tie to LO Learning Objective Today, we will review for the module 2 test. CFU Module 2 Why Move Things Around Concept Development Review Rigid Motion Transformations CFU Module 2 Why Move Things Around Concept Development Review Name the transformation CFU Module 2 Why Move Things Around Concept Development Review Name the transformation CFU Module 2 Why Move Things Around Concept Development Review Name the transformation CFU Module 2 Lesson 10: Sequences of Rigid Motions Concept Development Review 1. Triangle π΄π΅πΆ has been moved according to the following sequence: a translation followed by a rotation followed by a reflection. With precision, describe each rigid motion that would map β³ π΄π΅πΆ onto β³ π΄β² π΅β² πΆ β² . Use your transparency and add to the diagram if needed. Let there be the translation along vector π¨π¨β² so that π¨ = π¨β² . Let there be the clockwise rotation by π degrees around point π¨β² so that πͺ = πͺβ² and π¨πͺ = π¨β² πͺβ² . Let there be the reflection across π³π¨β² πͺβ² so that π© = π©β² . CFU Module 2 Lesson 11: Definition of Congruence and Some Basic Properties Concept Development Review 2. Is β³ π΄π΅πΆ β β³ π΄β² π΅β² πΆ β² ? If so, describe a sequence of rigid motions that proves they are congruent. If not, explain how you know. Sample response: Yes, β³ π¨π©πͺ β β³ π¨β² π©β² πͺβ² . Translate β³ π¨β² π©β² πͺβ² along vector π¨β²π¨. Rotate β³ π¨β² π©β² πͺβ² around center π¨, π degrees until side π¨β² πͺβ² coincides with side π¨πͺ. Then, reflect across line π¨πͺ CFU Module 2 Lesson 11: Definition of Congruence and Some Basic Properties Concept Development Review 3. Is β³ π΄π΅πΆ β β³ π΄β² π΅β² πΆ β² ? If so, describe a sequence of rigid motions that proves they are congruent. If not, explain how you know. Sample response: No, β³ π¨π©πͺ is not congruent toβ³ π¨β² π©β² πͺβ² , because π¨β² π©β² β π¨π©. We know that rigid motions preserve side length, there is no rigid motion that will allow π¨β² π©β² = π¨π©. CFU Module 2 Lesson 12: Angles Associated with Parallel Lines Concept Development Review Use the diagram to answer Questions 1 and 2. In the diagram, lines πΏ1 and πΏ2 are intersected by transversal π, forming angles 1β8, as shown. 4. If πΏ1 β₯ πΏ2 , what do know about β 2 and β 6? Use informal arguments to support your claim. They are alternate interior angles because they are on opposite sides of the transversal and inside of lines L1 and L2 . Also, the angles are equal in measure because the lines L1 and L2 are parallel. 5. If πΏ1 β₯ πΏ2 , what do know about β 1 and β 3? Use informal arguments to support your claim. They are corresponding angles because they are on the same side of the transversal and above each of lines L1 and L2 . Also, the angles are equal in measure because the lines L1 and L2 are parallel. CFU Module 2 Lesson 13: Angle Sum of a Triangle Concept Development Review 6. If πΏ1 β₯ πΏ2 , and πΏ3 β₯ πΏ4 , what is the measure of β 1? Explain how you arrived at your answer. The measure of angle π is ππ°. I know that the angle sum of triangles is πππ°. I already know that two of the angles of the triangle are ππ° and ππ°. CFU Module 2 Lesson 13: Angle Sum of a Triangle Concept Development Review 7. Given Line π΄π΅ is parallel to Line πΆπΈ, present an informal argument to prove that the interior angles of triangle π΄π΅πΆ have a sum of 180°. Since AB is parallel to CE, then the corresponding angles β BAC and β ECD are equal in measure. Similarly, angles β ABC and β ECB are equal in measure because they are alternate interior angles. Since β ACD is a straight angle, i.e., equal to 180° in measure, substitution shows that triangle ABC has a sum of 180°. Specifically, the straight angle is made up of angles β ACB, β ECB, and β ECD. β ACB is one of the interior angles of the triangle and one of the angles of the straight angle. We know that angle β ABC has the same measure as angle β ECB and that angle β BAC has the same measure as β ECD. Therefore, the sum of the interior angles will be the same as the angles of the straight angle, which is 180°. CFU Module 2 Lesson 14: More on the Angles of a Triangle Concept Development Review 8. Find the measure of angle π. Present an informal argument showing that your answer is correct. π = 35 + 32 π = 67° CFU Module 2 Lesson 14: More on the Angles of a Triangle Concept Development Review 9. Find the measure of angle π. Present an informal argument showing that your answer is correct. 155 = π + 128 π = 27° CFU Module 2 Lesson 14: More on the Angles of a Triangle Concept Development Review 10. Find the measure of angle π. Present an informal argument showing that your answer is correct. π = 103 + 18 π = 121° CFU Module 2 Why Move Things Around Concept Development Review What is the mβ π? By the straight angle definition, the other two angles of the triangle are 70° and 50°. So, by the angle sum theorem, π = 180° β 70° + 50° = 180° β 120° = 60°. CFU Module 2 Why Move Things Around Concept Development Review What is the mβ 1? mβ 1 = 88° What is the mβ 2? mβ 2 = 57° What is the mβ 4? mβ 4 = 145° CFU Module 2 Why Move Things Around Concept Development Review What is the mβ π? mβ π = 115° What is the mβ π? mβ π = 65° What is the mβ π? mβ π = 115° CFU Module 2 Why Move Things Around Homework 1. Study for module 2 end of module assessment. 2. Write or type one 8 ½β x 11β piece of paper with as many notes on it as youβd like. This is all you will be allowed to use on the exam. CFU