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niharika88028

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To visually prove that the sum of the three angles in a triangle is 180 degrees, you can create a simple geometric model using a few materials. Here’s a step-by-step working model you can easily create:

### Materials Needed:

- A large sheet of paper or cardboard (for the base)

- Protractor (for measuring angles)

- Ruler

- Pencil

- Scissors

- Glue or tape

- Markers or colored pencils (optional, for decoration)

### Instructions:

1. **Prepare the Base:**

- Take the large sheet of paper or cardboard and cut it into a triangle shape. You can make a triangle of any size, but a larger triangle might be easier to work with for this demonstration.

- Use a ruler and pencil to draw the outline of the triangle on the paper or cardboard. Cut out the triangle shape carefully.

2. **Divide the Triangle:**

- Using a pencil and ruler, draw three line segments (rays) starting from one vertex of the triangle. Each ray should extend outward, away from the triangle.

- Label these rays as \( \angle AOB \), \( \angle BOC \), and \( \angle COA \), where \( A, B, \) and \( C \) are the vertices of the triangle.

3. **Measure and Cut Angles:**

- Use the protractor to measure and mark angles \( \angle AOB \), \( \angle BOC \), and \( \angle COA \) on the rays you drew. Each angle should measure approximately 60 degrees.

- Cut out the angles \( \angle AOB \), \( \angle BOC \), and \( \angle COA \) carefully along the lines you marked.

4. **Arrange and Assemble:**

- Arrange the cut-out angles \( \angle AOB \), \( \angle BOC \), and \( \angle COA \) on the vertex where they originate (say, vertex \( A \)).

- Use glue or tape to attach the angles at vertex \( A \) such that they fit together perfectly to form a straight line (180 degrees).

5. **Display and Demonstrate:**

- Once the angles are attached, you can visually demonstrate that the angles fit together to form a straight line, which measures 180 degrees.

- Use markers or colored pencils to label the angles and sides of the triangle for clarity and educational purposes.

### Explanation:

By physically cutting out and arranging the angles \( \angle AOB \), \( \angle BOC \), and \( \angle COA \) at vertex \( A \), you visually demonstrate that they together form a straight line (180 degrees). This model effectively proves the theorem that the sum of the three angles in any triangle is always 180 degrees. It's a hands-on approach that helps in understanding the concept through tactile learning and visual representation.
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