What additional information is needed to prove the triangles congruent using SAS Congruency Theorem

Question

(1 point)
Responses

UW¯¯¯¯¯¯¯¯¯≅VL¯¯¯¯¯¯¯
line segment cap u cap w is congruent to line segment cap v liters

UL¯¯¯¯¯¯¯≅WV¯¯¯¯¯¯¯¯¯
line segment cap u liters is congruent to line segment cap w cap v

<L ≅
<W

<U ≅
<V

Answer 1

To prove two triangles congruent using the SAS (Side-Angle-Side) Congruency Theorem, you need the following information:

1. Two sides of one triangle are congruent to two sides of the other triangle: This means you need to establish that \( UW \cong VL \) and \( UL \cong WV \).

2. The angle included between those two sides: This means you need to demonstrate that the angle formed by the two given sides is congruent in both triangles, i.e., \( \angle L \cong \angle W \) should hold.

So, for the SAS Congruency Theorem to apply, you need to confirm the congruency of two sides and the angle between those sides in each triangle.

In your case:

• You have \( UW \cong VL \) and \( UL \cong WV \).
• You need to confirm \( \angle L \cong \angle W \) (for the angle between sides \( UW \) and \( UL \) in triangle U and \( VL \) and \( WV \) in triangle V).

If you confirm that \( \angle L \cong \angle W \) given the congruent sides, then the triangles are congruent by SAS.