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

Vocabulary Conditional Statement – “If…then”, , contains a hypothesis and conclusion Ex: If two angles are vertical angles, then they are congruent

If 2 angles are congruent, then they are vertical angles 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)

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

John lives in atl He lives in ga If john lives in ga, then he lives in atl If john doesn’t live in atl, then he doesn’t live in ga If john doesn’t live in ga, then he doesn’t live in atl

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

TRUE TRUE TRUE TRUE 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 TRUE TRUE TRUE TRUE

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