Question

if △abc is an isosceles triangle and d is the mid - point of (overline{ac}), what reason can be used to prove that the triangles are
sss
sas
asa
aas

Explanation:

In an isosceles triangle \(ABC\) with \(D\) as the mid - point of \(AC\), if we consider two sub - triangles formed (for example, \(\triangle ABD\) and \(\triangle CBD\)), we have \(AB = BC\) (by definition of isosceles triangle), \(AD=CD\) (since \(D\) is the mid - point of \(AC\)), and \(BD\) is common to both triangles. The Side - Side - Side (SSS) congruence criterion states that if three sides of one triangle are equal to three corresponding sides of another triangle, the two triangles are congruent. So SSS can be used to prove triangle congruence.

Answer:

SSS