Transcript Chapter 2.6 Notes: Prove Statements about Segments and Angles

Chapter 2.6 Notes: Prove
Statements about Segments and
Angles
Goal: You will write proofs using geometric
theorems.
• A proof is a logical argument that shows a satement
is true.
Two-Column Proofs:
• A two-column proof has numbered statements and
corresponding reasons that show an argument in a
logical order.
• In a two-column proof, each statement in the lefthand column is either given information or the result
of applying a known property or fact to statements
already made.
• Each reason in the right-hand column is the
explanation for the corresponding statement.
Writing a Two-Column Proof:
• In a proof, you make one statement at a time, until
you reach the conclusion.
• You are using deductive reasoning when you make
statements based on facts.
Given: m1  m3
Prove: mEBA  mDBC
Statements:
1. m1  m3
2. mEBA  m3  m2
3. mEBA  m1 m2
4. mDBC  m1  m2
5. mEBA  mDBC
Reasons:
1. Given
2. Angle Addition Post.
3. Substitution Property
4. Angle Addition Post.
5. Transitive Property
Theorems:
• The reasons used in a proof can include definitions,
properties, postulates, and theorems.
• A theorem is a statement that can be proven.
Ex.1: Write a two-column proof.
Given: M is the midpoint of AB
1
Prove: AM = AB
2
Ex.2: Write a two-column proof.
R
Given: RT = SU
Prove: RS = TU
S
T
U
Ex.3: Write a two-column proof.
Ex.4: Write a two-column proof.
Ex.5: Walking down a hallway at the mall, you notice
the music store is halfway between the food court
and the shoe store. The shoe store is halfway
between the music store and the bookstore. Prove
that the distance between the entrances of the food
court and the music store is the same as the
distances between the entrances of the shoe store
and the bookstore.
Ex.6: The distance from the park to the pool is the
same as the distance from your house to the school.
the school is between the pool and the house. Prove
that the distance from the park to the school is the
same as the distance from the pool to your house.