Question

1. what other information to do you need to prove ( \triangle abe cong \triangle eda ) by sss? ( \triangle eac ) is isosceles triangle with base ( overline{ec} ). ( angle e cong angle c ) ( \triangle eac ) is equilateral triangle. ( angle a cong angle c )

Explanation:

Step1: Recall SSS (Side - Side - Side) Congruence Criterion

SSS states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Step2: Analyze the given triangles \( \triangle ABE\) and \( \triangle EDA\)

We already know that \(AB = ED\) (from the markings on the figure). We need to find the condition that will give \(AE=EA\) (common side) and another pair of equal sides.
If \( \triangle EAC\) is an isosceles triangle with base \(EC\), then \(EA = CA\). But this is not relevant for \( \triangle ABE\) and \( \triangle EDA\).
If \( \angle E\cong\angle C\), this is an angle - related condition, not a side - related condition for SSS.
If \( \angle A\cong\angle C\), this is also an angle - related condition.
If \( \triangle EAC\) is an equilateral triangle, then \(EA = AC=EC\) and also \(EA = AC\). But more importantly, in \( \triangle ABE\) and \( \triangle EDA\), we have \(AB = ED\), \(AE = EA\) (common side) and if \( \triangle EAC\) is equilateral, then \(BE = DA\) (because \(AC\) is split into two equal parts \(AB\) and \(BC\) (since \(AB = ED\) and from equilateral \(AC = EC\) and using the properties of the figure's construction)).

Answer:

\(\triangle EAC\) is equilateral triangle.