CK12 - Geometry

The slopeof is 1. If you thinkof both of thesenumbersas fractions, and , you can tell that they
are oppositereciprocalsof eachother. Therefore,the two line segmentsare perpendicular.

Provingthis propertyin generalrequiresusingcongruenttriangles(surprise!).We will do this proofin two
parts.First,we will provethat one diagonal(connectingthe vertexangles)bisectsthe vertexanglesin the
kite.

Part 1:

• Given:Kite with and


• Prove: bisects and

Statement Reason

1. and 1. Given


2. 
   
   
   
   2. ReflexiveProperty
   
   
   3. SSS CongruencePostulate
   
   
   
   


3. 
   
   
   
   4. Correspondingpartsof congruenttrian-
      gles are congruent
   
   
   
   

4.

5. Correspondingpartsof congruenttrian-
   gles are congruent

5.

6. bisects and 6. Definitionof anglebisector

Now we will provethat the diagonalsare perpendicular.

Part 2:

• Given:Kite with and


• Prove: