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In her homework, Ysa needs to construct a figure that shows at least one right angle, at least one acute angle, and at least one obtuse angle. However, she needs to use only points A, B, C, D, and E. Would the figure be possible?
If yes, how should she do it? If no, explain.


Yes, it is possible for Ysa to construct a figure that meets the requirements using points A, B, C, D, and E. Here’s how she can do it:

### Construction Steps:
1. **Form a Triangle:**
   - Choose three points, say \( A \), \( B \), and \( C \), to form a triangle \( \triangle ABC \).
   - Adjust the position of these points to ensure that \( \angle ABC \) is a **right angle** (90°). This makes \( \angle BAC \) and \( \angle BCA \) both **acute angles** (less than 90°).

2. **Form a Quadrilateral:**
   - Choose another point \( D \) and place it outside of triangle \( ABC \).
   - Connect \( D \) to \( B \) and \( C \) to form quadrilateral \( ABCD \). 
   - Adjust the position of \( D \) so that one of the new angles, for example, \( \angle BCD \), is an **obtuse angle** (greater than 90°).

3. **Add the Fifth Point:**
   - Finally, add the fifth point \( E \) and place it inside or outside the figure \( ABCD \). 
   - Connect \( E \) to any of the points \( A \), \( B \), \( C \), or \( D \) if needed. This will not change the existing angles' nature, ensuring all angle types are represented.

### Explanation:
- **Right Angle:** This is formed at \( \angle ABC \) if the points \( A \), \( B \), and \( C \) are positioned such that \( \angle ABC = 90^\circ \).
- **Acute Angles:** The other two angles in the triangle \( \triangle ABC \) (i.e., \( \angle BAC \) and \( \angle BCA \)) will be acute since the sum of angles in a triangle is \( 180^\circ \), and one angle is already 90°.
- **Obtuse Angle:** By adjusting the position of point \( D \) outside triangle \( ABC \), an obtuse angle, such as \( \angle BCD \), can be created.

This construction will ensure that the figure has at least one right angle, one acute angle, and one obtuse angle.

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Would you like more details or have any questions?

### Related Questions:
1. What is the sum of all interior angles in a quadrilateral?
2. How can you ensure a triangle has a right angle?
3. What defines an acute angle?
4. What defines an obtuse angle?
5. How do you construct a quadrilateral with specific angle measurements?
6. What is the importance of point placement in angle construction?
7. Can a triangle have more than one obtuse angle?
8. How does adding an extra point affect the angles in a figure?

**Tip:** When constructing figures with specific angle requirements, sketching or using geometric tools can help visualize and ensure accuracy.

Learn how to construct a geometric figure with at least one right angle, one acute angle, and one obtuse angle using points A, B, C, D, and E. This geometry problem covers the construction of triangles and quadrilaterals, ensuring each angle type is represented accurately.

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