Final Answer:
The image explains which combinations of sides and angles guarantee a unique triangle (only one possible triangle can be drawn) and which do not.
✔ Unique triangles are guaranteed by:
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SSS — Three known side lengths
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SAS — Two sides and the angle between them
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ASA — Two angles and the side between them
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AAS — Two angles and any non-included side
✘ Not unique (can make more than one triangle):
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SSA — Two sides and a non-included angle (this is ambiguous — it might make 0, 1, or 2 triangles)
Example from image:
Given sides 6 and 11, and a 30° angle NOT between them → you can draw two different triangles (shown with green dashed lines). So SSA does NOT guarantee uniqueness.
This is why in geometry class, we learn SSS, SAS, ASA, AAS as “congruence shortcuts” — they prove triangles are identical. SSA is not on that list because it’s unreliable for proving uniqueness.
No calculations needed here — this is conceptual understanding based on triangle construction rules.
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Final Answer:
SSS, SAS, ASA, and AAS conditions guarantee a unique triangle. SSA does not — it may produce zero, one, or two different triangles.
Parent Tip: Review the logic above to help your child master the concept of side angle side worksheet.
