Congruent triangles are exact same triangles, but they might be placed at different positions. You can not use the SSS postulate or the SAS postulate to prove triangle ABC is congruent to triangle AED.
Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
Given that the ABE is a triangle. Now, in triangle ABC and triangle AED, there are two sides of the triangle that are congruent and a side. Therefore, the two triangles can be proved to be congruent only using the AAS Postulate.
Hence, You can not use the SSS postulate or the SAS postulate to prove triangle ABC is congruent to triangle AED.
Learn more about Congruent triangles:
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