Conditional Statements Notes Student Notes Vocabulary negation converse

Conditional Statements Notes: Student Notes Vocabulary: negation converse inverse contrapositive 10/26/10 ©Evergreen Public Schools 2010 1

Learning Target • I can write and identify the converse of a conditional statement, and determine whether the converse is true. • I can write and identify the inverse, and contrapositive of a conditional statement. Write a conditional statement. ©Evergreen Public Schools 2010 2

Launch What is the negation of a statement? • What does the phrase, “forget me not” mean? • Suppose I offer you a cookie, and you say, “ I don't want nothing”. Do you want me to give you a cookie or not? • Make a list of words that can be used for negation. ©Evergreen Public Schools 2010 3

Explore ©Evergreen Public Schools 2010 4

Negation of a Statement Write the negation of statement • Dogs are cats. • A fish has gills. • People can download songs from the internet. • The United States is governed by a king. Determine if the conditional statements and the negation are true or false. ©Evergreen Public Schools 2010 5

Negation of a Statement Write a conjecture about the validity the statement true or false) of each statement. ©Evergreen Public Schools 2010 (is 6

Find two ways to write the negation. • If a polygon is a quadrilateral then it has exactly four sides. • If a triangle is scalene then two angles are congruent. • If a parallelogram has four right angles then it must be a rectangle. Determine whether the statements are true or false. ©Evergreen Public Schools 2010 7

Inverse of a Conditional Statement If the United States is a republic, then the country is governed by a president. The inverse of the statement is • If the United States is not a republic, then the country is not governed by a president. ©Evergreen Public Schools 2010 8

Inverse of a Conditional Statement Write the inverse • If a polygon is a quadrilateral then it has exactly four sides. • If a triangle is scalene then two angles are congruent. • If a parallelogram has four right angles then it must be a rectangle. Determine whether the statements are true or false. ©Evergreen Public Schools 2010 9

Converse of a Conditional Statement Remember the converse? (We did this in Unit 1). • Write the converse of If the United States is a republic, then the country is governed by a president. ©Evergreen Public Schools 2010 10

Converse of a Conditional Statement Write the converse • If a polygon is a quadrilateral then it has exactly four sides. • If a triangle is scalene then two angles are congruent. • If a parallelogram has four right angles then it must be a rectangle. Determine whether the statements are true or false. ©Evergreen Public Schools 2010 11

Contrapositive of a Conditional Statement If the United States is a republic, then the country is governed by a president. The contrapositive of the statement is If the United States is not governed by a president then the country is not a republic. ©Evergreen Public Schools 2010 12

Contrapositive of a Conditional Statement Write the contrapositive • If a polygon is a quadrilateral then it has exactly four sides. • If a triangle is scalene then two angles are congruent. • If a parallelogram has four right angles then it must be a rectangle. Determine whether the statements are true or false. ©Evergreen Public Schools 2010 13

Contrapositive of a Conditional Statement Write a conjecture about the contrapositive of a conditional statement. ©Evergreen Public Schools 2010 14

Team Practice If a quadrilateral is a rhombus then its diagonals are perpendicular. Use the conditional statement above to write the • inverse • contrapositive ©Evergreen Public Schools 2010 15

Debrief Write your description for • negation • inverse • contrapositive ©Evergreen Public Schools

Learning Target Did you hit the target? • I can write and identify the converse of a conditional statement, and determine whether the converse is true. • I can write and identify the inverse, and contrapositive of a conditional statement. ©Evergreen Public Schools 2010 1 2 3 4 5 17