How to determine the converse inverse and contrapositive from a statement

The video tutorial explains the relationships between congruent and vertical angles through conditional statements. It covers the inverse, converse, and contrapositive of these statements, highlighting their logical equivalence. The tutorial also discusses how congruent angles can exist without being vertical, using corresponding angles as an example. The importance of understanding these logical relationships is emphasized for accurate reasoning in geometry.

What is the inverse of the statement: 'If two angles are congruent, then they are vertical angles'?

• If two angles are vertical, then they are congruent.

• If two angles are not vertical, then they are congruent.

• If two angles are not congruent, then they are not vertical angles.

• If two angles are congruent, then they are not vertical angles.

What does the converse of a statement involve?

• Only negating the hypothesis.

• Swapping and negating the hypothesis and conclusion.

• Swapping the hypothesis and conclusion.

• Negating both the hypothesis and conclusion.

Which of the following is true about contrapositive statements?

• They involve only negating the hypothesis.

• They are logically equivalent to the original statement.

• They involve only swapping the hypothesis and conclusion.

• They are always false if the original statement is true.

What can be said about congruent angles that are not vertical?

• They cannot exist.

• They are always corresponding angles.

• They can exist, such as corresponding angles.

• They are always supplementary.

If a conditional statement is false, what can be said about its contrapositive?

• It is sometimes true.

• It is unrelated to the original statement.

• It is also false.

• It is always true.