Question

a) additional known statement:

reason:

b) information still needed:

to prove the \\( \delta \cong \\) by \\( \underline{\text{sss}} \\)

Explanation:

Step1: Analyze the SSS (Side - Side - Side) congruence criterion

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

Step2: Identify the common side

In the given figure, \(XZ\) is a common side for \(\triangle DXZ\) and \(\triangle YXZ\). So, the additional known statement is \(XZ = XZ\) (Reflexive property of equality: a segment is equal to itself).

Step3: Determine the missing side

For SSS congruence of \(\triangle DXZ\) and \(\triangle YXZ\), we already know \(DX = YX\) (given by the marks on the sides). We have \(XZ = XZ\) (from Step 2). The missing side - length equality is \(DZ=YZ\).

Answer:

a) Additional Known Statement: \(XZ = XZ\); Reason: Reflexive property of equality.
b) Information still needed: \(DZ = YZ\)