Triangle Congruence Practice Worksheet - Identify congruent triangles and write the corresponding congruence statement for each pair.

It looks like you've uploaded an image containing a worksheet titled "Triangle Congruence Practice Problems" with 12 pairs of triangles, and the task is to determine whether each pair of triangles is congruent. If they are, you're supposed to write the reason (e.g., SSS, SAS, ASA, AAS, HL) and the triangle congruence statement (e.g., ΔABC ≅ ΔDEF).

Since I can't view images directly, I’ll help you solve this step-by-step based on typical problems of this type. However, if you describe each problem or provide details about the markings (like tick marks for sides, angle symbols, right angles, etc.), I can give precise answers.

But since I don’t have visual access, here’s how to approach such problems in general:

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🔍 How to Determine Triangle Congruence

Use the following congruence postulates:

1. SSS (Side-Side-Side) – All three sides are equal.
2. SAS (Side-Angle-Side) – Two sides and the included angle are equal.
3. ASA (Angle-Side-Angle) – Two angles and the included side are equal.
4. AAS (Angle-Angle-Side) – Two angles and a non-included side are equal.
5. HL (Hypotenuse-Leg) – Only for right triangles: hypotenuse and one leg are equal.

> ✔ Markings on diagrams:
> - Tick marks on sides → equal sides
> - Arcs on angles → equal angles
> - Right-angle symbols → 90° angles
> - Shared sides (like in overlapping triangles) → common side

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📌 General Strategy

For each pair:

1. Identify marked sides and angles.
2. Check which congruence rule applies.
3. Write the congruence statement using correct vertex order (matching corresponding parts).
4. If not enough info, write “Not congruent” or “Not enough information”.

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Example Problem (Typical Format)

Let’s say Problem 1 shows two triangles with:
- One side marked with a single tick mark,
- Another side with a double tick mark,
- And the included angle marked with an arc.

👉 Then it's SAS.

So answer would be:
> Yes, SAS
> ΔABC ≅ ΔDEF

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Common Patterns in These Types of Problems

| Pattern | Reason |
|--------|--------|
| Two triangles with all three sides marked equal | SSS |
| Two sides and included angle marked equal | SAS |
| Two angles and included side marked equal | ASA |
| Two angles and a non-included side marked equal | AAS |
| Right triangle with hypotenuse and one leg marked equal | HL |
| Overlapping triangles sharing a side | Use shared side as a common side (often part of SAS/ASA) |
| No matching markings or only one side/angle marked | Not congruent |

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Let Me Help You Solve It!

Please describe each problem (or just the ones you’re stuck on), including:

- How many sides are marked?
- Are there tick marks? Arcs? Right angles?
- Are the triangles overlapping?
- Any given labels?

For example:
> "Problem 1: Two triangles, ABC and DEF. AB = DE (one tick), BC = EF (two ticks), angle B = angle E (arc)."

Then I can tell you: Yes, SAS, ΔABC ≅ ΔDEF

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Alternatively, if you can copy-paste the text from the image (especially the labeled answers), I can verify them and explain why.

Let me know how you'd like to proceed!