Question

1. sss a) additional known statement: reason: b) information still needed: to prove the \\( \delta \cong \\) by \\( \underline{\text{sss}} \\)

Explanation:

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

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

Step2: Identify the Additional Known Statement

We know that \(EF = YX\) (marked with one tick) and \(GF=WX\) (marked with two ticks). For SSS, we need the third pair of sides. So, the additional known statement is \(EG = WY\). The reason is that in the SSS congruence criterion, we need all three pairs of corresponding sides to be equal.

Step3: Determine the Information Still Needed

Since we already have two pairs of sides (\(EF = YX\) and \(GF = WX\)) and we assume \(EG=WY\) (from part a), there is no other information needed. Because once we have all three pairs of sides equal (\(EG = WY\), \(EF = YX\), \(GF=WX\)), by the SSS congruence criterion, \(\triangle EGF\cong\triangle WYX\)

Answer:

a) Additional Known Statement: \(EG = WY\); Reason: For SSS (Side - Side - Side) congruence of triangles, all three pairs of corresponding sides must be equal.
b) Information still needed: None.