Question

Points C and D are equidistant from point A. Complete the following table to prove that AEC≅ AED

Answer 1

To prove that AEC≅ AED, we need to write following proofs or statement reasons.

It is given that points C and D are equidistant to point A. Hence,
AD ≅ AC

Next, CAE ≅ DAE. AE is the common side or the included side. 

Then, AE ≅ EA by Reflexive Property of Congruence as it is congruent to itself.

Lastly, EAD ≅ EAC by Symmetric Property of Congruence as these triangles are mirror image of each other.

Therefore, we can conclude that AEC≅ AED by SSS or Side-Side-Side. That is when all sides of triangles are congruent then both triangles are deemed to be equal.

Answer 2

Answer:

Step-by-step explanation:

Given: Points C and D are equidistant from point A.

To prove: AEC≅ AED

Proof:

It is given that points C and D are equidistant to point A. Hence,

AD ≅ AC

Now, CAE ≅ DAE. ( Because AE is the common side or the included side)

Then, AE ≅ EA (by Reflexive Property of Congruence )

Also, EAD ≅ EAC (by Symmetric Property of Congruence as these triangles are mirror image of each other)

Therefore, we can be concluded that AEC≅ AED by SSS rule of congruency.

Hence proved.