CK12 - Geometry

Noticethat in trapezoid , two baseanglesare markedas congruent.So, the trapezoidis
isosceles.That meansthat the two non-parallelsideshavethe samelength.Sinceyou are lookingfor the

lengthof , it will be congruentto. So, feet.

Diagonalsin IsoscelesTrapezoids

The anglesin isoscelestrapezoidsare importantto study. The diagonals,however, are also important.The
diagonalsin an isoscelestrapezoidwill not necessarilybe perpendicularas in rhombiand squares.They
are, however, congruent.Any time you find a trapezoidthat is isosceles,the two diagonalswill be congruent.

Theorem:The diagonalsof an isoscelestrapezoidare congruent

Example 3

Reviewthe two-columnproofbelow.

• Given: is a trapezoidand


• Prove:

Statement Reason

1. 
   
   
   
   1. Given
   
   
   2. Baseanglesin an isoscelestrapezoid
      are congruent
   
   
   
   

2.

3. 
   
   
   
   3. ReflexiveProperty.
   
   
   
   


4. 
   
   
   
   4. 
      
   
   
   5. Correspondingpartsof congruenttrian-
      gles are congruent
   
   
   
   

5.