2.4 Biconditional Statements

p <---> q means

p --> q and q --> p

Biconditional statement 2

If a point is a midpoint, then it divides the segment into two congruent segments.

Writing definitions as biconditional statements 1

Write each definition as a biconditional. A triangle is a three-sided polygon.

Identifying the conditionals within a biconditional statement

Write the conditional statement and converse within each biconditional. Two angles are congruent if and only if their measures are equal.

Polygon

A closed plane figure formed by three or more line segments. Each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear.

Writing definitions as biconditional statements answer 1

A figure is a triangle if and only if it is a three-sided polygon.

Quadrilateral

A four-sided polygon

Writing definitions as biconditional statements answer 2

A ray, segment, or line is a segment bisector if and only if it divides a segment into two congruent segments.

Writing definitions as biconditional statements 2

A segment bisector is a ray, segment, or line that divides a segment into two congruent segments.

Identifying the conditionals within a biconditional statement 2

A solution a is a base <--> it has a pH greater than 7.

Biconditional statement

A statement that can be written int he form "p if and only if q." This means "if p, then q" and "if q, then p."

Definition

A statement that describes a mathematical object and can be written as a true biconditional statements. Most definition in the glossary are not written as biconditional statements, but they can be. The "if and only if" is implied.

Triangle

A three-sided polygon

When you combine a conditional statement and its converse, you create a _______ ______.

Biconditional statement.

For a biconditional statement to be true, both the ______ ____ and its ____ must be true.

Conditional statement, converse

In geometry, biconditional statements are used to write ________.

Definitions.

Analyzing the truth value of a biconditional statement 1

Determine if each biconditional is true. If false, give a counterexample. A square has a side length of 5 if and only if it has an area of 25.

If either the conditional or the converse is false, then the biconditional statement is ____.

False.

Writing a biconditional statement 1

For each conditional, write the converse and a biconditional statement.