1. Triangles Triangles Exploration Activity Topic: Medians

2. Question to Answer What is a median? A line segment that joins the vertex of a triangle to the midpoint of its opposite side.

3. Question to Answer How many medians are in a triangle? Three

4. CONCEPTS TO KNOW All medians meet at a common point called a CENTROID. All medians meet at a common point called a CENTROID. The centroid always lie in the interior of the triangle. The centroid always lie in the interior of the triangle.

5. Statement to Explore Medians of a triangle concur. EXPLORATION ACTIVIY Objectives: To verify medians of a triangle concur at a point called a centroid, always lie in the interior of the triangle, by paper folding. To discover the property involving the segment lengths of medians by measuring segment parts with a ruler.

6. MATERIALS NEEDED:  COLORED PAPER  SCISSORS  RULER  MARKER OR COLORING PENCIL  PAPER AND PENCIL TO RECORD FINDINGS

7. STEP 1 Take a colored paper and draw any triangle ABC. Cut the triangle.

8. STEP 2 To get the mid point of BC, fold along BC, such that, point B coincides with C.

9. STEP 3 Unfold and mark the mid point of BC as M.

10. STEP 4 Form a crease joining AM. NOTE: AM is a median.

11. STEP 5 Similarly get medians BN and CP by paper folding. In your groups, discuss what you observe? Record your answer on notebook paper.

12. STEP 6 Take your ruler and measure the lengths for medians AM, BN, and CP. Record the lengths for each on your notebook paper. Take your ruler and measure the lengths for medians AM, BN, and CP. Record the lengths for each on your notebook paper. AM = _______ BN = _______ CP = _______

13. STEP 7 Mark and label point X as the centroid of your triangle. Mark and label point X as the centroid of your triangle. Now, measure and record the lengths of both segments of each median on your notebook paper. Now, measure and record the lengths of both segments of each median on your notebook paper. AX = _______ XM = _______ BX = _______ XN = _______ CX = _______ XP = _______

14. CONCLUSION  Discuss your findings from the previous slide in your group.  What pattern(s) do you see between the measured lengths of the two segments of the medians of the triangles? Between the median and each segment of the median? Write your conclusions on your notebook paper. Repeat the activity if needed.

15. ACTIVITY RESULT 1   Result : It is verified that themedians of a triangleconcur at a point called acentroid which always lie inthe interior of triangle.

16. ACTIVITY RESULT 2   Result: The centroid divides each median in the ratio 2:1. The segment from the centroid to the midpoint is a third of the length of the median. The segment from the centroid to the midpoint is a third of the length of the median. The segment from the centroid to the vertex is two thirds of the length of the median. The segment from the centroid to the vertex is two thirds of the length of the median.

17. Staple your triangle to your notebook paper. Turn your notebook paper in for a participation grade.

18. ACTIVITY LINK http://mykhmsmathclass.blogspot.com/2009/08/activ ity-medians-of-triangle-concur.html This activity can befound on the CMS Secondary Wiki High School Geometry Unit 3 – Triangles and Congruence See Resources Link Title: Medians of a Triangle Activity