To prove two triangles congruent using the SAS (Side-Angle-Side) Congruency Theorem, you need to show that:
- Two sides of one triangle are congruent to two sides of another triangle.
- The angle between those two sides in one triangle is congruent to the angle between the two sides in the other triangle.
From the information you provided:
- You need to confirm that you have two pairs of congruent sides and the angle between those sides.
- Specifically, you already have \( \overline{UL} \cong \overline{WV} \), and you need the angle measure between these sides to be congruent in both triangles, which is given as \( \angle U \cong \angle V \).
Thus, the additional information needed is to confirm that the angle formed by these two sides is congruent in both triangles.
For the second question regarding the SSS (Side-Side-Side) Congruency Theorem, to prove triangles congruent using SSS, you need to have the lengths of all three corresponding sides of one triangle being equal to the lengths of all three corresponding sides of the other triangle.
From the options provided:
- \( QR = EF \)
- \( PR = DF \)
These two pairs of equal sides are important, but you also need the length of the third pair of sides to be congruent.
So, the additional information you need to determine for SSS congruency is the length of the third side, which should be:
- \( PQ = DE \) (or the equivalent third side length).
In summary, for SAS, you need a congruent angle between the two sides you have; for SSS, you need the lengths of the third sides to be equal.
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