Worksheet on identifying congruent triangles using SSS, SAS, ASA, and AAS criteria.

Let’s go through each pair of triangles one by one.

We are checking if the triangles are congruent — meaning they have exactly the same size and shape. We can use rules like:

- SSS: All three sides equal.
- SAS: Two sides and the included angle equal.
- ASA: Two angles and the included side equal.
- AAS: Two angles and a non-included side equal.
- HL (for right triangles): Hypotenuse and one leg equal.

If none of these match, or if we don’t have enough info, then they’re not congruent or we can’t decide.

---

Pair A:
Left triangle: two sides = 8, included angle = 57°
Right triangle: two sides = 8, included angle = 57°
→ This is SAS → Congruent ✔

Pair B:
Both triangles have angles: 47°, 70°, 62° → all angles match.
But no side lengths given → we only know AAA → that’s not enough for congruence (could be different sizes).
→ Not enough information ✘

Pair C:
Left triangle: angles 68°, 59°, so third angle = 180 - 68 - 59 = 53°; side between 68° and 59° is 4.
Right triangle: angles 59°, 68°, so third angle = 53°; side between 59° and 68° is 4.5? Wait — let’s check positions.

Actually, in left triangle: side 4 is between 68° and 59° angles.
In right triangle: side 4.5 is between 59° and 68° angles → same angles, but side length different (4 vs 4.5) → not congruent.
Wait — maybe I misread. Let me recheck.

Left: angles at bottom left = 68°, bottom right = 59°, base = 4. So side between those two angles is 4.
Right: top angle = 59°, top right = 68°, top side = 4.5 → so side between 59° and 68° is 4.5.
So same two angles, but the side between them is different (4 vs 4.5) → not congruent.
→ Not congruent ✘

Pair D:
Both are right triangles.
Left: legs 6 and 9 → hypotenuse would be √(6²+9²) = √(36+81)=√117
Right: legs 6 and 9 → same → so SSS or SAS or HL → congruent ✔
Wait — actually, both have legs 6 and 9, right angle between them → SAS → congruent ✔

Pair E:
Left triangle: side 7, angle 52° — but we don’t know where the angle is relative to the side.
Right triangle: side 7, angle 52° — again, position unknown.
Could be SSA? Which is not a valid congruence rule unless it’s HL or specific cases.
Here, we don’t know if the angle is included or not.
→ Not enough information ✘

Pair F:
Left triangle: angles 52°, 56°, so third angle = 72°; side between 52° and 56° is 4.
Right triangle: angles 56°, 52°, so third angle = 72°; side between 56° and 52° is 4.
Same two angles and the included side → ASA → congruent ✔

Pair G:
Both are right triangles.
Left: one leg = 10, right angle shown.
Right: hypotenuse = 10? Or leg? The diagram shows the side labeled 10 is adjacent to the right angle → so it’s a leg.
But in left triangle, the side labeled 10 is also a leg.
However, we don’t know the other leg or hypotenuse.
Only one leg and right angle → not enough → not congruent or not enough info.
Wait — actually, both have a leg = 10 and right angle, but we don’t know the other side.
→ Not enough information ✘

Pair H:
Left triangle: sides 8 and 12, included angle 31°
Right triangle: sides 4 and 6, included angle 31°
Note: 8/4 = 2, 12/6 = 2 → same ratio, same angle → similar, but not congruent (different sizes).
→ Not congruent ✘

Pair I:
Left triangle: sides 5, 7, 9
Right triangle: sides 5, 7, 9 → same three sides → SSS → congruent ✔

Pair J:
Left triangle: sides 5 and 7, included angle 81°
Right triangle: sides 5 and 7, included angle 81° → same SAS → congruent ✔

---

Now let’s summarize:

A: Congruent (SAS)
B: Not enough info (AAA)
C: Not congruent (same angles, different side)
D: Congruent (SAS or HL)
E: Not enough info (SSA ambiguous)
F: Congruent (ASA)
G: Not enough info (only one leg and right angle)
H: Not congruent (similar, different size)
I: Congruent (SSS)
J: Congruent (SAS)

Final Answer:
A: Congruent
B: Not enough information
C: Not congruent
D: Congruent
E: Not enough information
F: Congruent
G: Not enough information
H: Not congruent
I: Congruent
J: Congruent