Understanding Angles and Proofs

The video tutorial explains two-column proofs, a method to organize thoughts for proving ideas. It covers setting up statements and reasons, starting with given information, and using definitions and properties like substitution and subtraction to reach a conclusion. The example demonstrates proving angles congruent by showing their measures are equal.

What is the main purpose of a two column proof?

• To solve algebraic equations

• To confuse the reader

• To list random statements

• To organize your thinking to prove an idea

Why are they called two column proofs?

• Because they are written in two different colors

• Because they are written on two pages

• Because they are organized into two columns

• Because they involve two people

What should be on the left column of a two column proof?

• Examples

• Diagrams

• Statements

• Reasons

What is the first step in a two column proof?

• List all possible reasons

• Write the conclusion

• Start with the given information

• Draw a diagram

What does the definition of supplementary angles state?

• Two angles that add up to 180°

• Two angles that are equal

• Two angles that are adjacent

• Two angles that add up to 90°

What property allows you to combine two equations that equal the same value?

• Division Property

• Multiplication Property

• Addition Property

• Substitution Property

What can you do if you have the same term on both sides of an equation?

• Subtract the term from both sides

• Add the term to both sides

• Multiply the term on both sides

• Divide the term on both sides

What does it mean if two angles are congruent?

• They have different measures

• They are supplementary

• They have equal measures

• They are adjacent

What symbol is used to denote congruent angles?

• ≠

• ≈

• =

• ≅

What should you always start with in a two column proof?

• The conclusion

• The given information

• A diagram

• A hypothesis