Let’s go through each triangle congruence rule shown in the image, one by one. We’ll explain what each acronym means and how you can tell if two triangles are congruent using that rule.
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1. SSS (Side-Side-Side)
This means: If all three sides of one triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent.
In the picture:
- Both triangles have marks on their sides: one tick, two ticks, and three ticks.
- The matching tick marks mean those sides are equal in length.
- Since all three sides match → triangles are congruent by SSS.
✔ So, SSS works when you know all 3 side lengths match.
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2. ASA (Angle-Side-Angle)
This means: If two angles and the side *between* them in one triangle are equal to the corresponding two angles and included side in another triangle, then the triangles are congruent.
In the picture:
- You see angle marks (arcs) and a side mark (tick) between them.
- The side is “included” — it’s right between the two angles.
- Matching angles + matching included side → congruent by ASA.
✔ Remember: The side must be BETWEEN the two angles for ASA.
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3. AAS (Angle-Angle-Side)
This means: If two angles and a non-included side (a side NOT between the two angles) in one triangle are equal to the corresponding parts in another triangle, then the triangles are congruent.
In the picture:
- Two angles are marked with arcs (same number of arcs = same measure).
- One side is marked with a tick — but this side is NOT between the two angles.
- That’s okay! AAS still proves congruence.
✔ Tip: AAS is like ASA, but the side is not between the angles — it’s next to one of them.
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4. SAS (Side-Angle-Side)
This means: If two sides and the angle *between* them in one triangle are equal to the corresponding two sides and included angle in another triangle, then the triangles are congruent.
In the picture:
- Two sides have matching tick marks.
- The angle between them has a matching arc mark.
- Side-Angle-Side in order → congruent by SAS.
✔ Important: The angle MUST be between the two sides for SAS.
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All four rules — SSS, ASA, AAS, SAS — are valid ways to prove that two triangles are congruent. Each requires specific matching parts, and as long as those parts match exactly (with correct positions), the whole triangles are identical in shape and size.
Final Answer:
The image shows four triangle congruence rules: SSS (three sides), ASA (two angles and the included side), AAS (two angles and a non-included side), and SAS (two sides and the included angle). All are valid methods to prove triangles are congruent when the specified parts match.
Parent Tip: Review the logic above to help your child master the concept of sss sas asa aas worksheet.
