Biconditional Statements th Monday August 19 and Definitions

Biconditional Statements th Monday August 19 and Definitions Logic and Conditional Statements Modules 1 -4 and 2 -1 p. 29 and p. 46 in your book Holt Geometry Holt Mc. Dougal Geometry

Biconditional Statements and Definitions Vocabulary Conditional Statement – “If…then”, , contains a hypothesis and conclusion Ex: If two angles are vertical angles, then they are congruent Holt Mc. Dougal Geometry

Biconditional Statements and Definitions Converse – interchange (flip) the hypothesis and conclusion If 2 angles are congruent, then they are vertical angles Inverse – Negate both hypothesis and conclusion If two angles are NOT vertical angles, then they are NOT congruent Contrapositive – Interchange & negate both hypothesis and conclusion If 2 angles are NOT congruent, then they are NOT vertical angles Holt Mc. Dougal Geometry

Biconditional Statements and Definitions True or False Conditional Statement – If 2 angles are vertical angles, then they are congruent Converse –If 2 angles are congruent, then they are vertical angles Inverse –If two angles are NOT vertical angles, then they are NOT congruent Contrapositive – If 2 angles are NOT congruent, then they are NOT vertical angles Holt Mc. Dougal Geometry

Biconditional Statements and Definitions On your own… Complete the statements for letters a – f and label each statement as “T” or “F” Holt Mc. Dougal Geometry

Biconditional Statements and Definitions A) If I receive a scholarship, then I will go to college • CONVERSE If I go to college, then I received a scholarship (FALSE) • INVERSE If I don’t get a scholarship, then I won’t go to college (FALSE) • CONTRAPOSITVE If I didn’t go to college, then I didn’t receive a scholarship (FALSE) Holt Mc. Dougal Geometry

Biconditional Statements and Definitions B) If a squares side is 5 cm, then its area is 25 cm 2 • CONVERSE If a squares area is 25 cm 2, then its side is 5 cm (TRUE) • INVERSE If a squares side is NOT 5 cm, then its area is NOT 25 cm 2 (TRUE) • CONTRAPOSITVE If a squares area is NOT 25 cm 2, then its side is NOT 5 cm (TRUE) Holt Mc. Dougal Geometry

Biconditional Statements and Definitions C) If they run a marathon, then they will feel exhausted • CONVERSE If they feel exhausted, then they ran a marathon (FALSE) • INVERSE If they don’t run a marathon, then they won’t feel exhausted (FALSE) • CONTRAPOSITVE If they don’t feel exhausted, then they didn’t run a marathon (TRUE) Holt Mc. Dougal Geometry

Biconditional Statements and Definitions D) If a figure is reflected, then its orientation changes. • CONVERSE If the orientation changes, then the figure was reflected (FALSE) • INVERSE If the figure isn’t reflected, then its orientation doesn’t change (FALSE) • CONTRAPOSITVE If a figures orientation doesn’t change, then the figure wasn’t reflected (TRUE) Holt Mc. Dougal Geometry

Biconditional Statements and Definitions E) If a quadrilateral is a rhombus, then its an equilateral • CONVERSE If a quad is equilateral, then it’s a rhombus(FALSE) • INVERSE If a quad is not a rhombus, then its not equilateral(FALSE) • CONTRAPOSITVE If a quad is not equilateral, then its not a rhombus (TRUE) Holt Mc. Dougal Geometry

Biconditional Statements and Definitions F) If a triangle is isosceles, then it is also equilateral • CONVERSE If a triangle is equilateral, then its isosceles(FALSE) • INVERSE If a triangle is not isosceles, then its not equilateral (FALSE) • CONTRAPOSITVE If a triangle is not equilateral, then its not isosceles (TRUE) Holt Mc. Dougal Geometry

Biconditional Statements th Tuesday August 20 and Definitions Logic and Conditional Statements Modules 1 -4 and 2 -1 p. 29 and p. 46 in your book Holt Geometry Holt Mc. Dougal Geometry

Biconditional Statements and Definitions Holt Mc. Dougal Geometry

Biconditional Statements and Definitions • If a conditional statement is true, then its converse is true • If a conditional statement is true, then its inverse is true • If a conditional statement is true, then its contrapositive is true Holt Mc. Dougal Geometry

Biconditional Statements and Definitions Biconditional Statement – When a conditional statement, its converse, inverse and contrapositive are all true. We can use the phrase “if and only if” (iff) or the symbol Holt Mc. Dougal Geometry

Biconditional Statements and Definitions • Ex: A pentagon is a five-sided polygon TRUE • Converse – If a figure is a five-sided polygon, then it’s a pentagon TRUE • Inverse – If a figure is NOT a pentagon, then its NOT five-sided polygon TRUE • Contrapositive – If a figure is NOT a fivesided polygon, then its NOT a pentagon TRUE • Biconditional – A figure is a pentagon if and only if it’s a five-sided polygon Holt Mc. Dougal Geometry

Biconditional Statements and Definitions On your own… Complete #’s 4 and 5 on the worksheet Holt Mc. Dougal Geometry

Biconditional Statements and Definitions 4) • The only statement that is a biconditional is letter b) If a square’s side is 5 cm, then its area is 25 cm 2 • A square’s side is 5 cm if and only if its area is 25 cm 2 Holt Mc. Dougal Geometry

Biconditional Statements and Definitions 5) • Biconditional Statement Examples… • A figure is a triangle if and only if it’s a polygon with three sides • An angle is a right angle if and only if it’s measure is exactly 900 Holt Mc. Dougal Geometry