Ask a New Question
Menu

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

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

<L ≅
<W

1 answer

To prove that two triangles are congruent using the SAS (Side-Angle-Side) Congruency Theorem, you need to have:

  1. Two pairs of corresponding sides (SAS): You need to show that two sides of one triangle are congruent to two sides of the other triangle.
  2. The included angle between those two sides: The angle formed between the two sides must also be proven to be congruent.

Based on your responses:

  • You have that \( UW \cong VL \) (one pair of sides).
  • You have \( UL \cong WV \) (the other pair of sides).
  • You also have the angles \( <U \cong <V \) and \( <L \cong <W \).

Conclusion:

Although you have several pairs of sides and angles listed, to use the SAS Theorem specifically, you need to focus on just one pair of sides (e.g., \( UW \) and \( VL \)), the second pair of sides (e.g., \( UL \) and \( WV \)), and specifically one of the angles between these two sides (e.g., either \( <U \) or \( <V \) as they would be the included angle between \( UW \) and \( UL \)).

If you clarify which specific sides and the specific included angle you wish to use, that is what is needed to apply the SAS Congruency Theorem. In essence, you must ensure that the angle you reference is indeed the angle between the two sides being compared.