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4.6 – Medians of a Triangle

4.6 – Medians of a Triangle. HW #10 Objectives #15, 16, 17. Intersecting Medians. -On a piece of paper, use a straightedge to draw a triangle (any type). -Then carefully cut out the triangle. -Label the vertices A, B and C. Intersecting Medians.

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4.6 – Medians of a Triangle

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  1. 4.6 – Medians of a Triangle HW #10 Objectives #15, 16, 17

  2. Intersecting Medians -On a piece of paper, use a straightedge to draw a triangle (any type). -Then carefully cut out the triangle. -Label the vertices A, B and C

  3. Intersecting Medians -Find the midpoint of each side by folding each side vertex to vertex, and pinch the paper in the middle. -Mark each midpoint.

  4. Intersecting Medians -Draw a segment from each vertex to the opposite midpoint. These segments are called medians. -Label D across from A, F across from B, and E across from C. (see right)

  5. Intersecting Medians Complete the table below using a ruler. Is there a relationship between the distance from P to a vertex and the distance from that vertex to the midpoint of the opposite side?

  6. Median of a Triangle • A median of a triangle is a segment from a vertex to the midpoint of the opposite side.

  7. Example 1 In ∆STR, draw a median from S to its opposite side. SOLUTION The side opposite S is TR. Find the midpoint of TR, and label it P. Then draw a segment from point S to point P. SP is a median of ∆STR. Draw a Median

  8. Checkpoint Sample answer: ANSWER Sample answer: ANSWER Sample answer: ANSWER Draw a Median Copy the triangle and draw a median. 1. 2. 3.

  9. Intersection of the Medians • The three medians of a triangle intersect at one point, called the centroid.

  10. Example 2 2 EA = DA = (27) = 18. 3 EA has a length of 18 and DE has a length of 9. ANSWER Use the Centroid of a Triangle E is the centroid of ∆ABC and DA=27. Find EA and DE. SOLUTION Using Theorem 4.9, you know that 2 Now use the Segment Addition Postulate to find ED. 3 DA = DE + EA Segment Addition Postulate 27 = DE + 18 Substitute 27 for DA and 18 for EA. 27 – 18 = DE + 18 – 18 Subtract 18 from each side. 9 = DE Simplify.

  11. Example 3 P is the centroid of ∆QRS and RP = 10. Find the length of RT. 3 . (10) = Multiply each side by 2 The median RT has a length of 15. ANSWER Use the Centroid of a Triangle SOLUTION 2 RP = RT Use Theorem 4.9. 3 3 3 2 2 2 2 3 3 Substitute 10 for RP. 10 = RT RT 15 = RT Simplify.

  12. Checkpoint Use the Centroid of a Triangle The centroid of the triangle is shown. Find the lengths. 4. Find BE and ED, given BD=24. Find JG and KG, given JK=4. 5. PQ=10; PN=30 BE=16; ED=8 JG=12; KG=8 ANSWER ANSWER ANSWER Find PQ and PN, given QN=20. 6.

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