The SAS (Side-Angle-Side) congruence theorem 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.
To justify the SAS theorem, you need a pair of triangles that demonstrate this property. Here’s what you generally look for in such pairs:
- Two triangles where:
- One pair of corresponding sides are equal in length.
- A pair of angles (the included angle) between those two sides are equal.
- The other pair of corresponding sides are also equal in length.
For example, consider triangles ABC and DEF:
- AB = DE (first side)
- Angle B = Angle E (included angle)
- AC = DF (second side)
If you have such pairs, you can justify SAS by showing that triangles ABC and DEF are congruent due to SAS.
If you provide specific pairs of triangles, I can help determine if they meet the criteria for SAS congruence!