One More Week Until Your Unit
Test!!!
1.
2.
3.
4.
Pick up notes from the front table
Take out your homework from last night and a
red pen.
Take out your whiteboard and whiteboard
marker.
Start writing down the learning objective:
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SWBAT write paragraph proofs.
SWBAT write a two-column proof given a
paragraph proof.
Learning Objective
SWBAT write paragraph proofs.
 SWBAT write a two-column proof given a
paragraph proof.

Math Joke of the Day
How is a geometry book like the United
Nations?
 They both have lots of rulers.

Whiteboards! APK

Fill in the blanks:
Given: 1 and 2 are right angles
Prove: 1  2
Statements
Reasons
1.
2. m1=90°
m2 = 90°
1. Given
2. .
3. .
4. 1  2
3. Trans Prop of =
4.
Whiteboards! APK Cont’d
Given: 1 and 2 are right angles
Prove: 1  2
Statements
Reasons
1. 1 and 2 are right
angles
1. Given
2. m1=90°
m2 = 90°
3. m 1 =m 2
4. 1  2
2. Def of right angle
3. Trans Prop of =
4. Def of  angles
Essential Question for Today

How would you compare and contrast
two-column and paragraph proofs?
The Past Couple of Days…
We learned how to write a two-column
proof!
 Today, we are going to learn a second way
of writing proofs, which are paragraph
proofs.
 Tomorrow, we are going to learn a third
method which is a flow-chart proof.

Paragraph Proofs
Just like writing paragraphs in English
class, we are going to write proofs in
complete sentences.
 You still must include EVERY step and the
reason behind each step.
 To begin, let’s make each step in a twocolumn proof it’s own sentence!

How to write a paragraph proof:
1.
2.
3.
Your first sentence should be the given
information ( home)
Each sentence must include both the
statement and the reason.
The last sentence should be what you
are trying to prove. (destination)
Let’s recall what we just did with our
whiteboards!: Right Angle Congruence Theorem
Now Let’s Write a Paragraph
Proof!
Given: 1 and 2 are right angles
Prove: 1  2
Statements
Reasons
1. 1 and 2 are right
angles
1. Given
2. m1=90°
m2 = 90°
3. m 1 =m 2
4. 1  2
2. Def of right angle
3. Trans Prop of =
4. Def of  angles
Right Angle Congruence Theorem
1.
Just like in a two-column proof, you
always start with the given information. (
our home)
1. It is given that 1 and 2 are right angles
2.
State the second step in a sentence
By the definition of right angles,
m1=90° and m2 = 90°
Now, let’s write this in Paragraph
form!
3.
State the 3rd step
By the transitive property of equality,
m 1 =m 2
4.
Remember, our last sentence should be
what we are trying to prove. ( our
destination)
By the definition of congruent angles,
1  2
Paragraph Proof of the Right Angle
Congruence Theorem

EXAMPLE
◦ It is given that 1 and 2 are right angles.
By the definition of right angles, m1=90°
and m2 = 90°. By the transitive
property of equality, m 1 =m 2. By the
definition of congruent angles, 1  2.

NON-EXAMPLE
◦ Because 1 and 2 are right angles, they
are congruent.
CFU
1.
What should the first sentence be in a
paragraph proof?
1.
What should the last sentence be in a
paragraph proof?
Writing a Paragraph Proof with your Table
Given: m1 + m2 = m4
Prove: m3 + m1 + m2 = 180°
Think About
What should your first sentence be?
 What should your last sentence be?
 How many sentences should there be?

Paragraph Proof
It is given that m1 + m2 =
m4. 3 and 4 are
supplementary by the Linear Pair
Theorem. So m3 + m4 = 180°
by definition of supplementary
angles. By Substitution, m3 +
m1 + m2 = 180°.
Vertical Angle Theorem

From what you know about vertical
angles, what do you predict the vertical
angle theorem to say?
◦ Think-pair-share
Vertical Angle Theorem
Vertical angles are congruent
Now Let’s Write a Two-Column
Prove Given a Paragraph
Given: 1 and 3 are vertical
angles
Prove: 1  3
Paragraph Proof:
 1 and  3 are vertical angles. By the definition of vertical
angles,  1 and  3 are formed by intersecting lines.
Therefore,  1 and  2 are a linear pair and  2 and  3
are a linear pair by the definition of linear pairs. By the
Linear Pair Theorem,  1 and  2 are supplementary, and 
2 and  3 are supplementary. So by the Congruent
Supplements Theorem,  1 is congruent to  3.
•
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What do you think the first statement
should be in your two column proof?
Talk with your table!
How many steps do you think there
are in this two-column proof?
Fill this Two-Column Proof Out
based on your Paragraph proof
Challenge!
You just proved the Vertical Angles
Theorem. 
 Can you prove it another way?

◦ First write it as a two-column proof
◦ Then write it in paragraph form
◦ Work with your table!
Let’s Share!
On a Separate Piece of Paper Write
this Proof in Paragraph Form
Given: 1  4
Prove: 2  3
Directions:
1. First write this as a two-column proof
individually.
2. Then write this in paragraph form
Whiteboards!
1. How many sentences do
you think there will be in
this paragraph proof?
2. Write the first sentence
of this paragraph proof.
3. Write the second
sentence.
4. Write the 3rd sentence.
5. Write the 4th sentence.
Closure
On the bottom of your notes, write down
the similarities and differences of twocolumn proofs and paragraph proofs.
 Which type do you prefer? Why?
 What is your first sentence of a paragraph
proof? If a two-column has 5 steps, how
many sentences does the paragraph proof
have?
 Be ready to share out.
