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

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

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

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

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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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