Pearson Unit 1 Topic 2: Reasoning and Proof 2-3: Biconditionals and Definitions Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.

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Presentation transcript:

Pearson Unit 1 Topic 2: Reasoning and Proof 2-3: Biconditionals and Definitions Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

TEKS Focus: (4)(B) Identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse. (1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.

When you combine a conditional statement and its converse, you create a Biconditional Statement. This statement can be written in the form “p if and only if q.” This means “if p, then q” and “if q, then p.” Symbolically this is written as p q means p q and q p. In geometry, biconditional statements are used to write definitions.

BICONDITIONAL BICONDITIONAL p q definition reversible Single true statement BICONDITIONAL p q has two parts true conditional true converse

Biconditional Statements

If an animal is an insect, then __________ _______________________________________ ________________________________________ it has six legs and three body parts.

Converse: Biconditional: If they are congruent, then two angles have equal measure. Two angles are congruent if and only if they have equal measure.

two numbers are reciprocals, their product is 1. Condtional 1: If ____________________________________________________________ then __________________________________________________________________ Condtional 2: two numbers are reciprocals, their product is 1. their product is 1, two numbers are reciprocals.

Example: 2 ½ : Write each definition as a biconditional. A. A triangle is a three sided polygon. A polygon is a triangle if and only if it has three sides. B. Parallel lines are two coplanar lines that never intersect. Two coplanar lines are parallel if and only if they never intersect. C. Four coplanar points lie in the same plane. Four points are coplanar if and only if they lie in the same plane.

Condtional 1: If ____________________________________________________________, then __________________________________________________________________ Condtional 2: Biconditional: ___________________________________________________ ___________________________________________________________________ an angle is a straight angle the angle measures 180. an angle measures 180 the angle is a straight angle. An angle is a straight angle if and only if the angle measures 180.

Example 4: 3 if and

Example 5: If you live in Austin, then you live in Texas. You live in Austin if and only if you live in Texas. If you live in Austin, then you live in Texas. If you live in Texas, then you live in Austin. The biconditional is FALSE. TRUE FALSE

Example 6: D

Example 7: Is the following a good definition. If not, rewrite so that it is. A square is a figure with four right angles. A quadrilateral is a square if and only if it has four right angles and four congruent sides.