CK12 - Geometry

Statement Reason

1. is an isoscelestrapezoidwith 1. Given


2. Extend 2. Line Postulate


3. Construct as shownin the figure 3. ParallelPostulate

belowsuchthat

with addedauxiliarylinesand

markings

4. is a parallelogram 4. Definitionof a parallelogram


5. 
   
   
   
   5. Oppositeanglesin a parallelogramare
   
   
   6. Oppositesidesof a parallelogramare
      congruent
   
   
   
   

6.

7. Definitionof isoscelestriangle


8. is isosceles


9. 
   
   
   
   8. Baseanglesin an isoscelestriangleare
   
   
   
   


10. 
    
    
    
    9. AlternateInteriorAnglesTheorem
    
    
    
    


11. 
    
    
    
    10. TransitivePropertyof
    
    
    
    


12. 
    
    
    
    11. TransitivePropertyof
    
    
    
    

IdentifyIsoscelesTrapezoidswith BaseAngles

In the last lesson,you learnedaboutbiconditionalstatementsand conversestatements.You just learned
thatif a trapezoidis an isoscelestrapezoidthen baseanglesare congruent.The converseof this statement
is also true. If a trapezoidhas two congruentanglesalongthe samebase,then it is an isoscelestrapezoid.
You can use this fact to identifylengthsin differenttrapezoids.

First,we provethat this converseis true.

Theorem:If two anglesalongone baseof a trapezoidare congruent,then the trapezoid

is an isoscelestrapezoid

•

Given:Trapezoid with and

• Prove: