https://file.aiquickdraw.com/mathbot/file/1725854506711qzv5vdd0.pdf

The document you provided is a geometry and trigonometry homework assignment with short response and development questions. Here's an overview of the structure:

### General Instructions
- The homework consists of two parts distributed over three pages, with a total value of 79 points.
- The answers need to be submitted as a PDF file, including all procedures and justifications for each solution.
- Collaboration with other groups is not allowed, and clarity and order in the presentation are essential.

### Part I: Short Responses (Value: 52 points)
This section includes six questions with various subparts, focusing on:
1. **Right Triangle Properties** (△EDB):
   - Calculating angles, similarity of triangles, and lengths.
2. **Triangle Bisector and Properties** (△ABC):
   - Determining angle relations, checking conditions for an equilateral triangle, and proving triangle similarity.
3. **Scalene Triangle Proportions**:
   - Solving for the sides of a scalene triangle using the golden ratio (\(\phi = 1 + \frac{\sqrt{5}}{2}\)).
4. **Parallel Lines and Angle Bisectors**:
   - Calculating segment lengths and angles using parallel line properties and bisectors.
5. **Centroid in Triangles**:
   - Determining segment lengths and properties using the centroid.
6. **Linear Pair of Angles and Areas**:
   - Calculating angles and areas of triangles based on given geometric properties.

### Part II: Development (Value: 27 points

Geometry and trigonometry homework, focused on right triangles, scalene triangles, bisectors, centroids, and parallel line properties.

Explore a detailed geometry and trigonometry homework assignment covering right triangles, scalene triangles, centroids, and angle bisectors. Perfect for high school students, this assignment focuses on triangle similarity, the golden ratio, and centroid properties.

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