Holt McDougal Geometry Biconditional Statements and Definitions Monday August 19 th Holt Geometry Logic and Conditional Statements Logic and Conditional

Holt McDougal Geometry

Biconditional Statements and DefinitionsMonday August 19th

Holt Geometry

Logic and Conditional StatementsLogic and Conditional Statements

Modules 1-4 and 2-1Modules 1-4 and 2-1

p. 29 and p. 46 in your bookp. 29 and p. 46 in your book



Biconditional Statements and Definitions

Conditional Statement – “If…then”, , contains a hypothesis and conclusion

Ex: If two angles are vertical angles, then they are congruent

Vocabulary



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



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



On your own…

Complete the statements for letters a – f and label each statement

as “T” or “F”



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)



B) If a squares side is 5cm, then its area is 25cm2

• CONVERSE If a squares area is 25cm2, then its side is 5cm (TRUE)

• INVERSE If a squares side is NOT 5cm, then its area is NOT 25cm2 (TRUE)

• CONTRAPOSITVE If a squares area is NOT 25cm2, then its side is NOT 5cm (TRUE)



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)



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)



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)



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)


Biconditional Statements and DefinitionsTuesday August 20th

Holt Geometry

Logic and Conditional StatementsLogic and Conditional Statements

Modules 1-4 and 2-1Modules 1-4 and 2-1

p. 29 and p. 46 in your bookp. 29 and p. 46 in your book






• 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



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



• Ex: A pentagon is a five-sided polygon

• Converse – If a figure is a five-sided polygon, then it’s a pentagon

• Inverse – If a figure is NOT a pentagon, then its NOT five-sided polygon

• Contrapositive – If a figure is NOT a five-sided polygon, then its NOT a pentagon

• Biconditional – A figure is a pentagon if and only if it’s a five-sided polygon



On your own…

Complete #’s 4 and 5 on the worksheet



4)

• The only statement that is a biconditional is letter b) If a square’s side is 5cm, then its area is 25cm2

• A square’s side is 5cm if and only if its area is 25cm2



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

Documents

Holt McDougal Geometry Biconditional Statements and Definitions Monday August 19 th Holt Geometry Logic and Conditional Statements Logic and Conditional