Congruent Triangles Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Congruent Triangles" with six pairs of triangles (labeled a through f), and the task is to state the postulate or theorem to prove each pair of triangles congruent.

Since I can't view images directly, I’ll guide you on how to solve this type of problem and explain the common methods used to prove triangle congruence. Then, if you describe the diagrams (e.g., which sides or angles are marked as equal), I can help identify the correct postulate for each pair.

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🔷 Triangle Congruence Postulates/Theorems

To prove two triangles are congruent, we use one of these five criteria:

1. SSS (Side-Side-Side) – All three sides of one triangle are congruent to the corresponding sides of another.
2. SAS (Side-Angle-Side) – Two sides and the included angle of one triangle are congruent to the corresponding parts of another.
3. ASA (Angle-Side-Angle) – Two angles and the included side are congruent.
4. AAS (Angle-Angle-Side) – Two angles and a non-included side are congruent.
5. HL (Hypotenuse-Leg) – For right triangles only: Hypotenuse and one leg are congruent.

> Note: AAA (Angle-Angle-Angle) proves similarity, not congruence.

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🔎 How to Analyze Each Pair

For each pair of triangles (a–f), look for:
- Marked equal sides (usually shown with tick marks)
- Marked equal angles (usually shown with arcs)
- Whether there’s a right angle (indicated by a square corner)

Then match the markings to one of the above postulates.

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📌 Example Walkthrough (if I could see the image):

Let’s suppose:

#### a) Two triangles with two sides and the included angle marked
→ Use SAS

#### b) Two triangles with all three sides marked equal
→ Use SSS

#### c) Two triangles with two angles and the side between them marked
→ Use ASA

#### d) Two triangles with two angles and a non-included side marked
→ Use AAS

#### e) Right triangles with hypotenuse and one leg marked equal
→ Use HL

#### f) Two triangles with three angles marked but no sides — then they’re not necessarily congruent
→ Not enough info (only AAA → similar, not congruent)

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✔ Your Next Step

Please describe each diagram in words, such as:

> "In figure a), both triangles have two sides marked with one tick mark each, and the angle between them is marked with an arc."

Or send a text description of what's drawn in each pair.

Once I know the markings, I can tell you the correct postulate for each.

Let me know!