Exploring Properties, Postulates, and Theorems in Mathematics

The video tutorial guides students through identifying various mathematical properties, postulates, theorems, and definitions. It covers the symmetric property, segment and angle addition postulates, definition of congruency, subtraction and substitution properties, reflexive and symmetric properties, and vertical and linear pair theorems. The tutorial also explains how to write two-column and paragraph proofs, providing examples and encouraging students to use their handouts for reference.

Which property allows you to reverse the order of congruent angles?

• Substitution Property

• Transitive Property

• Symmetric Property

• Reflexive Property

What postulate allows you to add the lengths of segments to get the total length?

• Angle Addition Postulate

• Segment Addition Postulate

• Transitive Property

• Symmetric Property

Which postulate allows you to add the measures of two angles to get the total angle?

• Transitive Property

• Angle Addition Postulate

• Segment Addition Postulate

• Symmetric Property

What definition allows you to change from a congruency to an equal sign?

• Substitution Property

• Definition of Congruency

• Symmetric Property

• Transitive Property

Which property is used when you subtract the same number from both sides of an equation?

• Addition Property

• Subtraction Property

• Transitive Property

• Symmetric Property

If two angles are both equal to 32 degrees, which property can be used to conclude they are equal to each other?

• Symmetric Property

• Substitution Property

• Reflexive Property

• Transitive Property

Which property states that something is equal to itself?

• Reflexive Property

• Symmetric Property

• Transitive Property

• Substitution Property

What theorem states that vertical angles are congruent?

• Linear Pair Theorem

• Vertical Angle Theorem

• Angle Addition Postulate

• Segment Addition Postulate

Which theorem tells us that linear pairs are supplementary?

• Vertical Angle Theorem

• Linear Pair Theorem

• Segment Addition Postulate

• Angle Addition Postulate

When writing a two-column proof, what do you need to provide for each step?

• Both the solution and the reasons

• Only the reasons

• Only the solution

• Neither the solution nor the reasons