What additional information is needed to prove the triangles congruent using SAS Congruency Theorem (1 point) Responses UL¯¯¯¯¯¯¯≅WV¯¯¯¯¯¯¯¯¯ line segment cap u liters is congruent to line segment cap w cap v <U ≅ <V <L ≅ <W UW¯¯¯¯¯¯¯¯¯≅VL¯¯¯¯¯¯¯

Answer 1

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

1. The Length of One Side: You need to confirm that the lengths of the two sides included between the two triangles (which are already being considered) are congruent. Specifically, you have:

   • \( UL \cong WV \) (this is one side),
   • To prove the triangles are congruent, we need either \( UW \cong VL \) or to establish the size of those segments if they are not already given.

2. The Measure of the Included Angle: You need to establish that the angle between the two given sides is congruent. This means showing:

   • \( \angle U \cong \angle V \) (or whichever angles correspond to the included sides).

In summary, to apply the SAS theorem, you need two sides of one triangle to be congruent to two sides of another triangle, and the included angle between those sides must also be congruent. Make sure to specify which sides and angles need to be established to complete the proof.