Question

Suppose AB=AE Can you use the sss Postulate or the SAs Postulate to prove ABC= AED ?

Answer 1

Answer: both apply

Explanation:

• SSS congruence postulate says that if three sides of one triangle are congruent to three sides of other triangle then the triangles are said tobe congruent.

SAS congruence postulate says that if two sides and the included angle of a triangle are congruent to two sides and the included angle of other triangle then the two triangles are said to be congruent.

In the given triangles ΔABC and ΔAED , we have

∠BAC ≅ ∠EAD

AC ≅ AD

BE ≅ DE

If AB ≅ AE , then we have sufficient things to proof that ΔABC ≅ ΔAED by SSS congruence postulate .

i.e. for AC ≅ AD , BE ≅ DE and AB ≅ AE [all three sides are congruent]

ΔABC ≅ ΔAED by SSS congruence postulate.

Also, If AB ≅ AE , then we have sufficient things to proof that ΔABC ≅ ΔAED by SAS congruence postulate .

i.e. for AC ≅ AD [Side]

∠BAC ≅ ∠EAD [included angle]

AB ≅ AE [Side]

⇒ ΔABC ≅ ΔAED by SAS congruence postulate.

Hence, we can apply both postulates to prove triangles congruent .

Answer 2

Option 4 is correct that is both apply

Explanation:

We have given the triangle we have to tell which postulate SSS or SAS to use to prove

ΔABC=ΔAED

We can use both of them

Case1: Since, three of the sides are equal that is

AB=AE

AC=AD

BC=ED

Which means SSS can be used

Since, SSS is side side side

Case2: Since one angle and two sides are equal

AB=AE

AC=AD

And ∠BAC=∠EAD

Which means SAS can be used

Since, SAS is side angle side

Therefore, Option 4 is correct that is both apply.