Benzel
Investigative Geometry
Section 2.5 Learning Ladder- Segment Proofs
BELL WORK
(1) Solve for the following and provide a reason for each step in the process. You may use flow
charts or statement reason format:
4(x – 5) = x + 4
(2) Determine if the argument uses the Law of Detachment, the Law of Syllogism, or neither
• If I go to the movie, then I’ll eat popcorn.
• If I eat popcorn, then I’ll enjoy the movie
• If I go to the movie, then I’ll enjoy the movie.
Benzel’s Trait of The Week: The Power of Positivity- I know that this is a busy time
of year and everything is heating up. I would like you to come in with a positive
attitude as this will help you feel better in the time coming up before
benchmarks.
The Geometric Proof Playbook!
(One of the Most Important Documents You’ll EVER Own In Geometry)
Advice
Tip
Things to Think About
(1) Visualize what you need to prove
(2) Start with the beginning and ending
first
(3) Know and identify key vocabulary
words surrounding your proofs- Use
your playbook!
(4) Know the difference between
equality and congruence. We set
measurements equal. We set line
segments and angles congruent
The ACTUAL Playbook!
In Geometry, we write about Line Segments AND Angles. Here are some
Properties
Segment Rules
Angle Rules
Reflexive
Symmetric
Transitive
Addition
Section 2.5 – Proving Statements about Segments
Theorem:
Two-Column Proof:
Properties of Segment Congruence
Reflexive:
Symmetric:
Transitive:
Examples:
1. Prove the Symmetric Property of Segment Congruence.
Given: PQ  XY
Prove: XY  PQ
Statements
Reasons
1. PQ  XY
1. Given
2.
2. Definition of congruent segments
3.
3.
4.
4.
2. In the figure below, prove that EG  FH if we are given EF = GH.
E
F
G
H
Statements
Reasons
1.
1.
2. EF + FG = GH + FG
2.
3. EG = EF + FG,
FH = GH + FG
4.
3.
5.
5.
3. Complete the proof.
Given: RT  WY , ST  WX
Prove: RS  XY
4. Substitution Property of Equality
W
Statements
R
S
X
Y
Reasons
1. RT  WY
1. Given
2. RT = WY
2.
3. RT = RS + ST;
WY = WX + XY
4. RS + ST = WX + XY
3.
5. ST = WX
5. Given
6. RS = XY
6.
7.
7. Definition of congruent segments
4.
Now, rewrite the proof in paragraph form. Just rewrite your statements and reasons in
complete sentences!
T
Proof Homework!
Directions: Fill in the reasons for the proofs below. Use your Playbook!
1.
Given: ∠𝐶𝐷𝐸 and ∠𝐸𝐷𝐹 are supplementary
Solve for x.
Statements
2.
1.
∠𝐶𝐷𝐸 and ∠𝐸𝐷𝐹 are supplementary
2.
𝑚∠𝐶𝐷𝐸 + 𝑚∠𝐸𝐷𝐹 = 180
3.
𝑥 + (3𝑥 + 20) = 180
4.
4𝑥 + 20 = 180
5.
4𝑥 = 160
6.
𝑥 = 40
Reasons
Given: XY = 42
Solve for n.
Statements
1.
XY = 42
2.
XZ + ZY = XY
3.
3(𝑛 + 4) + 3𝑛 = 42
4.
3𝑛 + 12 + 3𝑛 = 42
5.
6𝑛 + 12 = 42
6.
6𝑛 = 30
7.
𝑛=5
Reasons
3.
̅̅̅̅.
Given: C is the midpoint of 𝐴𝐷
Prove: x = 6
Statements
1.
C is the midpoint of ̅̅̅̅
AD.
2.
̅̅̅̅
𝐴𝐶 ≅ ̅̅̅̅
𝐶𝐷
3.
𝐴𝐶 = 𝐶𝐷
4.
4𝑥 = 2𝑥 + 12
5.
6.
Reasons
Definition of congruent segments
Subtraction Property of Equality
Learning Ladder Rubric:
The purpose of the learning ladder is to make you into a highly effective student. Remember, we are
investigators! Here is the rubric in which you will get your daily participation grade:
Requirement
Completes Bell
Work
Beginning (1)
- Bell work is
mainly
incomplete.
_____/5
Takes Effective
Notes
_____/5
Practices
Purposefully
_____/5
- Notes are
totally
incomplete
with many
examples not
written down.
- It is apparent
that student is
not
productively
spending class
time as evident
by heads down
or side
conversations
Practice
problems and
homework are
not done
Approaching
(3)
- Bellwork is
partially
complete with
the answer but
not shown
work.
OR
- Bell work is
not completed
silently and
independently.
- Notes are only
partially
complete.
- Student is on
occasion off
task.
Practice
problems and
homework are
only partially
done OR
Little to no
work is shown.
Mastered (4)
Advanced (5)
- Bell Work is
completed
silently and
independently
- Bell work has
some shown
work.
- Bell work is
completed with
detailed shown
work.
- Notes are
mainly
complete with
a few small
missing details
- Notes are
complete and
even show
signs of active
engagement:
- Writing
questions on
the sides of the
notes
- Highly
detailed
- Great class
participation.
Practice
problems are
mainly done
with some
work shown.
However, there
is room for
more shown
work.
Practice
problems and
homework is
done with
sufficient
shown work.
TOTAL _____/15