Question

1. sas

a) additional known statement:

reason:

b) information still needed:

to prove the $\delta \cong$ by $\underline{sas}$

Explanation:

Step1: Analyze the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Determine the additional known statement for part (a)

Since we have right - angled triangles (\(\angle U=\angle X = 90^{\circ}\)) and one pair of sides (the marked equal sides). The additional known statement is \(VU=ZY\). The reason is that we already have \(\angle U=\angle X\) (right angles) and one pair of sides (from the marking). To use SAS, we need another pair of sides.

Step3: Determine the information still needed for part (b)

We already have one pair of sides (marked equal) and right angles (\(\angle U=\angle X\)). For SAS, we still need \(WU = XY\) (the other pair of sides that form the right - angle)

Answer:

a) Additional Known Statement: \(VU = ZY\)
Reason: To satisfy one of the side conditions for the SAS congruence criterion (already having the right - angle as the included angle and one side from the marking)
b) Information still needed: \(WU=XY\)