Geometry worksheet featuring six problems where students must determine if triangles are congruent and cite the appropriate theorem.

Since I can't view or access images directly, I can’t see the specific triangles or markings in your uploaded worksheet. However, I can help you solve Congruent Triangles problems based on typical geometry worksheets like this one.

Let me guide you through how to solve such problems step by step, and you can apply it to your image:

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🔷 Problem Overview:

You are given several pairs of triangles (labeled A–F), and for each pair, you must:
1. Determine if the triangles are congruent.
2. If yes, state the congruence postulate used (SSS, SAS, ASA, AAS, HL).
3. If not, write "not possible" and explain why.

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🔷 Step-by-Step Guide:

#### ✔ Step 1: Understand the Congruence Postulates
| Postulate | Meaning |
|---------|--------|
| SSS | All three sides are equal |
| SAS | Two sides and the included angle are equal |
| ASA | Two angles and the included side are equal |
| AAS | Two angles and a non-included side are equal |
| HL | Right triangles: Hypotenuse and one leg are equal |

> Note: AAA is NOT a congruence postulate — only similarity.

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#### ✔ Step 2: Analyze Each Pair

Let’s assume your worksheet has six diagrams labeled A–F. For each, look at the marks on the triangles:
- Tick marks = equal sides
- Arcs = equal angles
- Right-angle symbols = 90° angles
- Labels (like AB = DE) may also be given

Then match them to the postulates.

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🧩 Example Walkthrough (Typical Problems):

#### 🔹 Problem A:
```
Triangle ABC and Triangle DEF
AB = DE (marked with one tick)
BC = EF (marked with two ticks)
AC = DF (marked with three ticks)
```
✔ Answer:
- Congruent? Yes
- Postulate: SSS
- Reason: All three sides are marked equal.

---

#### 🔹 Problem B:
```
Triangle ABC and Triangle DEF
∠A = ∠D (arc mark)
AB = DE (one tick)
AC = DF (one tick)
```
✔ Answer:
- Congruent? Yes
- Postulate: SAS
- Reason: Two sides and the included angle are equal.

---

#### 🔹 Problem C:
```
Triangle ABC and Triangle DEF
∠A = ∠D (arc)
∠B = ∠E (arc)
Side BC = EF (tick mark)
```
✔ Answer:
- Congruent? Yes
- Postulate: AAS
- Reason: Two angles and a non-included side.

> ⚠️ Note: If the side was between the two angles → ASA. But here, BC is opposite ∠A, so it's AAS.

---

#### 🔹 Problem D:
```
Triangle ABC and Triangle DEF
Only one side and one angle marked
No enough info
```
✘ Answer:
- Congruent? Not possible
- Reason: Not enough information to apply any postulate.

---

#### 🔹 Problem E:
```
Two right triangles
Hypotenuse AB = DE
Leg AC = DF
```
✔ Answer:
- Congruent? Yes
- Postulate: HL (Hypotenuse-Leg)
- Reason: Right triangles with hypotenuse and one leg equal.

---

#### 🔹 Problem F:
```
Triangle ABC and Triangle DEF
Only two angles marked equal
No sides marked
```
✘ Answer:
- Congruent? Not possible
- Reason: AAA only proves similarity, not congruence. Need at least one side.

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✔ Final Tips:

- Always check what is marked (sides, angles, right angles).
- Match the pattern to SSS, SAS, ASA, AAS, or HL.
- Never assume anything not shown.
- Write full statements: “Yes, by SAS” or “Not possible – insufficient information.”

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📝 Format Your Answers Like This:

For each triangle pair:

a) Are they congruent?
→ Yes / No
b) If yes, state postulate:
→ SSS / SAS / ASA / AAS / HL
c) Reason:
→ Brief explanation (e.g., "All three sides are marked equal")

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👉 If you can describe the markings (e.g., "Triangle A has two sides with ticks and an included angle marked") or transcribe the diagram details, I can give you exact answers for your worksheet!

Just tell me what's in each diagram (A-F), and I’ll solve it fully.