Geo 2.1 conjectures and counterexamples

Front

What is a counterexample?

Back

A counterexample is an example that disproves a statement or proposition. It shows that the statement is not always true.

Front

Define a conditional statement.

Back

A conditional statement is a logical statement that has two parts: a hypothesis (if part) and a conclusion (then part). It is often written in the form 'If P, then Q'.

Front

What is the hypothesis in a conditional statement?

Back

The hypothesis is the part of the conditional statement that follows 'if'. It represents the condition that must be met.

Front

What is the conclusion in a conditional statement?

Back

The conclusion is the part of the conditional statement that follows 'then'. It represents the result or outcome if the hypothesis is true.

Front

Provide an example of a conditional statement.

Back

If it rains, then the ground will be wet.

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P'. It is logically equivalent to the original statement.

Front

What is a biconditional statement?

Back

A biconditional statement is a statement that combines two conditional statements, stating that both conditions are true. It is written as 'P if and only if Q'.

Front

How do you identify a valid counterexample?

Back

A valid counterexample must satisfy the hypothesis of the conditional statement but not the conclusion.

Front

What does it mean for angles to be congruent?

Back

Two angles are congruent if they have the same measure.

Front

What is the relationship between congruent angles and their measures?

Back

If two angles are congruent, then their measures are equal.