Given: quadrilateral abcd is a kite. prove: δaed ≅ δced it is given that quadrilateral abcd is a kite. we know that line ad ≅ line cd by the definition of ( by the kite diagonal theorem, line ac is ( to line bd this means that angles aed and ced are right angles. we also see that line ed ≅ line ed by the ( property. therefore, we have that δaed ≅ δced by ( 1. a) kite b) congruent c) quadrilateral 2. a) congruent b) parallel c) perpendicular 3. a) congruency b) reflexive c) substitution 4. a) aas b) hl c) sas

Step-by-step explanation:

One

The definition of a kite.

Two

Perpendicular. The diagonals meet at right angles

Three

I don't know if the term is still used, but when I first learned this material (many years ago) we called it the reflexive property.

Four

You found out that <AED = <CED which established that both are right angles. The problem is, you do not have enough information to prove SAS.

AAS is never a dependable reason for proving anything conguent.

HL is really your only choice.

In this question we have to prove the ΔAED ≅ ΔCED by filling up the appropriate option.

Given that :

Quadrilateral ABCD is a kite.

Prove :

ΔAED ≅ ΔCED

It is given that quadrilateral ABCD is a kite. We know that line AD ≅ line CD by the definition of (1)__kite___. By the kite diagonal theorem, line AC is (2)_perpendicular_ to line BD This means that angles AED and CED are right angles.

          Reason:  The diagonals intersect at right angles.

We also see that line ED ≅ line ED by the (3)__reflexive___ property.  

         Reason: Reflexive property of equality means that anything is equal                                    to itself.    

Therefore, we have that ΔAED ≅ ΔCED by (4)__SAS__.

         Reason: SAS rule states that, if two sides and the one angle of one            triangle are equal to 2 sides and 1 angle of other triangle , then the triangles   are congruent.

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