Question

1. sss

to prove the \\( \delta \cong \\) by sas
a) additional known statement:

reason:

b) information still needed:

to prove the \\( \delta \cong \\) by sss

Explanation:

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

The SSS congruence criterion 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

For triangle \(RST\) and triangle \(XYZ\), we already know that \(RS = XY\) (from the single hash mark) and \(ST=YZ\) (from the triple hash mark).

Step3: Determine the additional known statement

The additional known statement is \(RT = XZ\). The reason is that in the SSS congruence, we need the third pair of sides to be equal.

Step4: Determine the information still needed (if any)

Since we are using SSS, if we assume we are comparing \(\triangle RST\) and \(\triangle XYZ\), and we have \(RS = XY\), \(ST = YZ\), the information still needed (if not already given) is \(RT=XZ\) (but in part (a) we are giving an additional known statement. If we consider the general SSS for two triangles, once we have two pairs of sides equal, the third pair is what is needed. But in the context of the problem structure:

• For part (a), if we assume the two triangles \(\triangle RST\) and \(\triangle XYZ\), the additional known statement (assuming some prior information) could be \(RT = XZ\) with the reason of SSS requirement (to have three pairs of equal sides).
• For part (b), if we assume we know two pairs of sides (say \(RS = XY\) and \(ST=YZ\)), the information still needed is the equality of the third pair of sides (\(RT = XZ\))

Answer:

a) Additional Known Statement: \(RT = XZ\); Reason: SSS (Side - Side - Side) congruence criterion requires three pairs of equal sides.
b) Information still needed: \(RT = XZ\)