Passage-1:

2) Exterior angle 180° interior angle

4) Each exterior angle

In AABC, AD, BE, CF are medians and G is the centroid of AABC. Let G divides median in the ratio 2:1

24. AD,BE and CF are medians of a AABC and BE + CF > kBC then

To analyze the passage and extract the underlying mathematical concepts:

### Passage-1 Breakdown:
1. **Exterior Angle of a Polygon**: 
   - The phrase "Exterior angle 180° interior angle" suggests that the relationship between exterior and interior angles is being explored.
   - The sum of an exterior angle and its corresponding interior angle of any polygon equals 180° since they are supplementary angles.

2. **Each Exterior Angle**: 
   - This may be referring to the fact that for a regular polygon, the measure of each exterior angle is given by:
   \[
   \text{Exterior angle} = \frac{360^\circ}{n}
   \]
   where \( n \) is the number of sides of the polygon.

3. **Centroid of a Triangle (AABC)**:
   - In the triangle \( \Delta ABC \), medians \( AD \), \( BE \), and \( CF \) intersect at point \( G \), which is the centroid.
   - The centroid divides each median in the ratio 2:1, meaning the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side.

4. **Inequality Involving Medians**: 
   - The condition "BE + CF > kBC" suggests an inequality involving the lengths of the medians. Generally, medians are greater than half the length of the side, so \( k \) could be a constant related to the properties of medians and triangle side lengths.

### Additional Information:
- The centroid is known as the center of gravity or balance point of the triangle.
- The sum of any two medians in a triangle is greater than the length of the third side. This follows from the triangle inequality theorem applied to medians.

### Next Steps:
You can explore further details, such as:
1. What is the value of \( k \) for the inequality involving medians?
2. How do the medians of a triangle relate to its side lengths?
3. Can you provide a geometric proof that the centroid divides each median in a 2:1 ratio?
4. What are the properties of exterior and interior angles in polygons?
5. How does the inequality \( BE + CF > kBC \) apply to different types of triangles (e.g., equilateral, scalene)?

**Tip**: Remember that the medians of a triangle always intersect at the centroid, which divides the triangle into six smaller triangles of equal area.

2) Exterior angle 180° interior angle
4) Each exterior angle
In AABC, AD, BE, CF are medians and G is the centroid of AABC. Let G divides median in the ratio 2:1
24. AD, BE, and CF are medians of a AABC and BE + CF > kBC then

Explore the relationship between exterior and interior angles in polygons and the properties of the centroid in triangles. Learn how medians divide a triangle and how the centroid divides each median in a 2:1 ratio. Suitable for students in Grades 9-11.

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