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Module 2
Why Move Things Around
Activating Prior Knowledge –
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 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 𝑨𝑨′ 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 𝑳𝑨′ 𝑪′ so that
𝑩 = 𝑩′ .
CFU
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
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
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 𝐿1 and 𝐿2 are
intersected by transversal 𝑚, forming angles 1–8, as shown.
4. If 𝐿1 ∥ 𝐿2 , 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 L1 and L2 . Also, the angles are equal in
measure because the lines L1 and L2 are parallel.
5. If 𝐿1 ∥ 𝐿2 , 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 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 𝐿1 ∥ 𝐿2 , and 𝐿3 ∥ 𝐿4 , 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
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
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
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
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
Module 2
Why Move Things Around
Concept Development Review
What is the m∠𝑝?
By the straight
angle definition, the
other two angles of
the triangle are 70°
and 50°.
So, by the angle sum theorem,
𝑝 = 180° − 70° + 50° = 180° − 120° = 60°.
CFU
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
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
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