Activating Prior Knowledge – Module 2 Why Move Things Around Activating Prior Knowledge – What are rigid motion transformations? Tie to LO

Today, we will review for the module 2 test. Learning Objective Today, we will review for the module 2 test. CFU

Concept Development Review Rigid Motion Transformations Module 2 Why Move Things Around Concept Development Review Rigid Motion Transformations CFU

Concept Development Review Module 2 Why Move Things Around Concept Development Review Name the transformation CFU

Concept Development Review Module 2 Why Move Things Around Concept Development Review Name the transformation CFU

Concept Development Review Module 2 Why Move Things Around Concept Development Review Name the transformation CFU

Concept Development Review Module 2 Lesson 10: Sequences of Rigid Motions Concept Development Review 1. Triangle 𝐴𝐵𝐶 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 △𝐴𝐵𝐶 onto △ 𝐴 ′ 𝐵 ′ 𝐶 ′ . Use your transparency and add to the diagram if needed. Let there be the translation along vector 𝑨 𝑨 ′ so that 𝑨= 𝑨 ′ . Let there be the clockwise rotation by 𝒅 degrees around point 𝑨 ′ so that 𝑪= 𝑪 ′ and 𝑨𝑪= 𝑨 ′ 𝑪 ′ . Let there be the reflection across 𝑳 𝑨 ′ 𝑪 ′ so that 𝑩= 𝑩 ′ . CFU

Concept Development Review Module 2 Lesson 11: Definition of Congruence and Some Basic Properties Concept Development Review 2. Is △𝐴𝐵𝐶≅ △ 𝐴 ′ 𝐵 ′ 𝐶 ′ ? If so, describe a sequence of rigid motions that proves they are congruent. If not, explain how you know.  Sample response: Yes, △𝑨𝑩𝑪≅△ 𝑨 ′ 𝑩 ′ 𝑪 ′ . Translate △ 𝑨 ′ 𝑩 ′ 𝑪 ′ along vector 𝑨′𝑨 . Rotate △ 𝑨 ′ 𝑩 ′ 𝑪 ′ around center 𝑨, 𝒅 degrees until side 𝑨 ′ 𝑪 ′ coincides with side 𝑨𝑪. Then, reflect across line 𝑨𝑪 CFU

Concept Development Review Module 2 Lesson 11: Definition of Congruence and Some Basic Properties Concept Development Review 3. Is △𝐴𝐵𝐶≅ △ 𝐴 ′ 𝐵 ′ 𝐶 ′ ? If so, describe a sequence of rigid motions that proves they are congruent. If not, explain how you know. Sample response: No, △𝑨𝑩𝑪 is not congruent to△ 𝑨 ′ 𝑩 ′ 𝑪 ′ , because 𝑨 ′ 𝑩′ ≠ 𝑨𝑩 . We know that rigid motions preserve side length, there is no rigid motion that will allow 𝑨 ′ 𝑩′ = 𝑨𝑩 . CFU

Concept Development Review 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 𝐿 1 and 𝐿 2 are intersected by transversal 𝑚, forming angles 1–8, as shown. 4. If 𝐿 1 ∥ 𝐿 2 , what do know about ∠2 and ∠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 L 1 and L 2 . Also, the angles are equal in measure because the lines L 1 and L 2 are parallel. 5. If 𝐿 1 ∥ 𝐿 2 , what do know about ∠1 and ∠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 L 1 and L 2 . Also, the angles are equal in measure because the lines L 1 and L 2 are parallel. CFU

Lesson 13: Angle Sum of a Triangle Concept Development Review Module 2 Lesson 13: Angle Sum of a Triangle Concept Development Review 6. If 𝐿 1 ∥ 𝐿 2 , and 𝐿 3 ∥ 𝐿 4 , what is the measure of ∠1? Explain how you arrived at your answer. The measure of angle 𝟏 is 𝟐𝟗°. I know that the angle sum of triangles is 𝟏𝟖𝟎°. I already know that two of the angles of the triangle are 𝟗𝟎° and 𝟔𝟏°. CFU

Lesson 13: Angle Sum of a Triangle Concept Development Review Module 2 Lesson 13: Angle Sum of a Triangle Concept Development Review 7. Given Line 𝐴𝐵 is parallel to Line 𝐶𝐸, present an informal argument to prove that the interior angles of triangle 𝐴𝐵𝐶 have a sum of 180°. Since AB is parallel to CE, then the corresponding angles ∠BAC and ∠ECD are equal in measure. Similarly, angles ∠ABC and ∠ECB are equal in measure because they are alternate interior angles. Since ∠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 ∠ACB, ∠ECB, and ∠ECD. ∠ACB is one of the interior angles of the triangle and one of the angles of the straight angle. We know that angle ∠ABC has the same measure as angle ∠ECB and that angle ∠BAC has the same measure as ∠ECD. Therefore, the sum of the interior angles will be the same as the angles of the straight angle, which is 180°. CFU

Lesson 14: More on the Angles of a Triangle Concept Development Review Module 2 Lesson 14: More on the Angles of a Triangle Concept Development Review 8. Find the measure of angle 𝑝. Present an informal argument showing that your answer is correct. 𝑝=35+32 𝑝=67° CFU

Lesson 14: More on the Angles of a Triangle Concept Development Review Module 2 Lesson 14: More on the Angles of a Triangle Concept Development Review 9. Find the measure of angle 𝑞. Present an informal argument showing that your answer is correct. 155=𝑞+128 𝑞=27° CFU

Lesson 14: More on the Angles of a Triangle Concept Development Review Module 2 Lesson 14: More on the Angles of a Triangle Concept Development Review 10. Find the measure of angle 𝑟. Present an informal argument showing that your answer is correct. 𝑟=103+18 𝑟=121° CFU

Concept Development Review Module 2 Why Move Things Around Concept Development Review By the straight angle definition, the other two angles of the triangle are 70° and 50°. What is the m∠𝑝? So, by the angle sum theorem, 𝑝=180°− 70°+50° =180°−120°=60°. CFU

Concept Development Review Module 2 Why Move Things Around Concept Development Review What is the m∠1? m∠1=88° What is the m∠2? m∠2=57° What is the m∠4? m∠4=145° CFU

Concept Development Review Module 2 Why Move Things Around Concept Development Review What is the m∠𝑐? m∠𝑐=115° What is the m∠𝑑? m∠𝑑=65° What is the m∠𝑓? m∠𝑓=115° CFU

CFU Why Move Things Around Homework Module 2 Why Move Things Around Homework 1. Study for module 2 end of module assessment. 2. Write or type one 8 ½” x 11” piece of paper with as many notes on it as you’d like. This is all you will be allowed to use on the exam. CFU