CK12 - Geometry

2. Since is isosceles,we have.


3. By angleaddition,we have.


4. So , and by substitution.


5. Notethat is exteriorto , so.


6. Hence, and , we have.

We can also provea similartheoremaboutangles.

Largeranglehas longeroppositeside:If one angleof a trianglehas greatermeasure

than a secondangle,then the side oppositethe first angleis longerthan the side opposite

the secondangle.

Proof. In orderto provethe theorem,we will use a methodthat relieson indirectreasoning,a methodthat
we will explorefurther. The methodrelieson startingwith the assumptionthat the conclusionof the theorem
is wrong,and then reachinga conclusionthat logicallycontradictsthe givenstatements.

1. Consider with. We mustshowthat.


2. Assumetemporarilythat is not greaterthan. Theneither or.


3. If , then the anglesat vertices and are congruent.This is a contradictionof our given
   statements.