6.1 Inequalities and Indirect Proofs. Up until now we have dealt with sides and angles that are ___ and have used the properties of _.

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Presentation transcript:

6.1 Inequalities and Indirect Proofs

Up until now we have dealt with sides and angles that are ___________ and have used the properties of _________ in our proofs. Now we will deal with _________ sides and angles. We will be using properties of ______________.

Property of Inequality (All of these)

Exterior Angle Theorem: ____________ __________________________________

A B C D E

F D E 1

6.3 Indirect Proof

We will be using __________________ _____________________________. Lets look at an example. Lets suppose after walking home, Joe enters the house carrying a dry umbrella. You can conclude that it is not raining outside. Why? ________________________________

Steps for solving an Indirect Proof: _________________________________ __________________________________ _________________________________ __________________________________ __________________________________ __________________________________

Lets try one, these will be written as a paragragh. S R P Q __________________________________________

6.4 Inequalities

Inequalities for one Triangle Theorem 6.2:__________________________ ________________________________________ Theorem 6.3:__________________________ ________________________________________

A B C List angles from Largest to smallest: ____ ____ ____ A BC List sides from Largest to smallest: ____ ____ ____

Corollary 1: ______________________________ ________________________________________ Theorem 6.4: ___________________________ ________________________________________

When given 2 sides of a triangle you can find a range that the third side will be between. _____________________________________ ______________________________________

Find out if each is a triangle, given the sides: 1. 6,8, , 5, , 4, , 4, , 5, 6

80 xx-10 B AC Which side is the longest?

A B C D

6.5 Inequalities for 2 Triangles

Theorem 6-5: SAS Inequality _____________________________________ _____________________________________ _____________________________________ A B

Theorem 6-5: SSS Inequality _____________________________________ _____________________________________ _____________________________________ A B

Example: What can you deduce? 1 2 R T V S ____________ ____________ _____________ _____________ _____________

Example: What can you deduce? R T V S ______________ Y X 12 14

Example: What can you deduce? 5 10 ______________