Direct answer
Start with the two sides you are given. The included angle is the angle where those two sides meet, so it sits between them. For SAS, match those two sides and that angle between them in the other triangle.
What SAS requires
SAS means side-angle-side: two adjacent sides and the angle between them. To prove two triangles congruent by SAS, the two sides and the included angle in one triangle must equal the matching two sides and included angle in the other triangle.
For students working through a diagram, the order does not begin at one special point. Begin with the marked information: identify the two given sides, then find the angle formed by those same sides.
How to find the included angle
Look at the endpoints of the first given side, then the endpoints of the second given side. The shared endpoint is the vertex of the included angle. The angle at that vertex is the one to use for SAS.
A useful check is to ask: “Do both given sides touch this angle?” If they do, it is the included angle. If one or both sides do not touch the angle, it is not the angle required for SAS.
How to match corresponding sides
Once you have found the included angle in each triangle, match the sides that form that angle. Each side beside the included angle in one triangle should match a side beside the included angle in the other.
Keep the same relationship in both triangles: side, angle between the sides, side. This helps students avoid choosing a correct-looking angle that is not between the two stated sides.
Why SSA is not SAS
SSA gives two sides and an angle, but the angle is not necessarily between those sides. That difference matters because SSA may allow multiple solutions, while SAS uses the included angle between the two sides.
What to do next
Review the cited sources and apply the relevant guidance described above.
Sources
- How To Prove Triangles Congruent - SSS, SAS, ASA, AAS Rules (video lessons, examples and solutions)
- SAS Triangle Calculator
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