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.