Triangle congruence worksheet | TPT - Free Printable

It looks like you've uploaded a worksheet titled "Proving Triangles Congruent using SSS, SAS, ASA and AAS". However, since I can't view images directly, I can’t see the specific diagrams or problems in your image.

But based on the structure of the worksheet (as described in your text), I can help you solve typical problems of this type. Let me explain how to approach such problems and provide examples for each congruence postulate: SSS, SAS, ASA, and AAS.

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🔷 Goal:

For each pair of triangles, determine if they are congruent using one of the following postulates:
- SSS: Side-Side-Side (all three sides equal)
- SAS: Side-Angle-Side (two sides and included angle equal)
- ASA: Angle-Side-Angle (two angles and included side equal)
- AAS: Angle-Angle-Side (two angles and non-included side equal)

Then, write the congruence statement and reason.

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Let’s go through each problem as it appears from your description:

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🔹 Problem 1:

> ΔABC ≅ ΔDEF
> Given: AB = DE, BC = EF, AC = DF

✔ This is SSS (all three sides are congruent).
✔️ Congruence Statement: ΔABC ≅ ΔDEF
✔️ Reason: SSS

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🔹 Problem 2:

> ΔABC ≅ ΔDEF
> Given: ∠A ≅ ∠D, AB ≅ DE, AC ≅ DF

✔ Two sides and the included angle are congruent → SAS
✔️ Congruence Statement: ΔABC ≅ ΔDEF
✔️ Reason: SAS

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🔹 Problem 3:

> ΔABC ≅ ΔDEF
> Given: ∠A ≅ ∠D, ∠B ≅ ∠E, AB ≅ DE

✔ Two angles and the included side → ASA
✔️ Congruence Statement: ΔABC ≅ ΔDEF
✔️ Reason: ASA

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🔹 Problem 4:

> ΔABC ≅ ΔDEF
> Given: ∠A ≅ ∠D, ∠C ≅ ∠F, BC ≅ EF

✔ Two angles and a non-included side → AAS
✔️ Congruence Statement: ΔABC ≅ ΔDEF
✔️ Reason: AAS

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🔹 Problem 5:

> ΔABC ≅ ΔDEF
> Given: CD = CE, ∠D = ∠E, AD = BE

Wait — this seems ambiguous. But likely, it's showing two triangles sharing a common side or overlapping.

Assume:
- Triangle ADC and triangle BEC
- CD = CE (given)
- ∠D ≅ ∠E (given)
- AD = BE (given)

If we're comparing ΔADC and ΔBEC:
- AD = BE
- CD = CE
- ∠D = ∠E

So, two sides and the included angle? Wait — is the angle between them?

Yes! If ∠D is between AD and CD, and ∠E is between BE and CE, then:

✔ SAS applies → ΔADC ≅ ΔBEC

✔️ Congruence Statement: ΔADC ≅ ΔBEC
✔️ Reason: SAS

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🔹 Problem 6:

> ΔABC ≅ ΔDEF
> Given: AB = DE, ∠A ≅ ∠D, ∠B ≅ ∠E

We have:
- ∠A ≅ ∠D
- ∠B ≅ ∠E
- AB ≅ DE

This is ASA (two angles and the included side).

✔️ Congruence Statement: ΔABC ≅ ΔDEF
✔️ Reason: ASA

(Alternatively, could be AAS, but since AB is between ∠A and ∠B, it's ASA.)

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## ✔ Summary Table:

| Problem | Given Info | Postulate | Congruence Statement |
|--------|------------|-----------|------------------------|
| 1 | Three sides equal | SSS | ΔABC ≅ ΔDEF |
| 2 | Two sides, included angle | SAS | ΔABC ≅ ΔDEF |
| 3 | Two angles, included side | ASA | ΔABC ≅ ΔDEF |
| 4 | Two angles, non-included side | AAS | ΔABC ≅ ΔDEF |
| 5 | Two sides, included angle | SAS | ΔADC ≅ ΔBEC |
| 6 | Two angles, included side | ASA | ΔABC ≅ ΔDEF |

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💡 Tips:

- SSS: All three sides.
- SAS: Two sides + included angle (the angle between them).
- ASA: Two angles + included side.
- AAS: Two angles + non-included side (same as ASA in logic, but order matters).
- Always check corresponding parts — label vertices carefully!

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If you can describe the actual diagrams (e.g., which triangles, what is marked), I can give exact answers for your specific worksheet.

Would you like to describe the figures or type out the given information for each problem?