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Mid-Segment & Triangle Proportionality

Mid-Segment & Triangle Proportionality. Day 8. A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle . In the figure  D  is the midpoint of and E  is the midpoint of  . So ,  is a midsegment. Triangle Midsegment theorem.

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Mid-Segment & Triangle Proportionality

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  1. Mid-Segment & Triangle Proportionality Day 8

  2. A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle. In the figure D is the midpoint of andE is the midpoint of  . So,  is a midsegment.

  3. Triangle Midsegment theorem • A midsegment connecting two sides of a triangle is parallel to the third side and is half as long. IfAD = DB and AE = EC, then and

  4. Example 1 • Given DE is the length of the mid-segment.  Find AB. Solution:The mid-segment is half of the third side. 7 is half of 14. AB = 14. 

  5. Example 2 Given DE is the length of the mid-segment.  Find AB. Solution: AB = 16m

  6. Example 3 • Given XYis the length of the mid-segment. Solve for x. Solution: ½ (18) = (2x-6) 9 = 2x – 6 15 = 2x 7.5 = x

  7. Triangle Proportionality theorem • If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally. • If

  8. Example 4 Find the value of x. The lines   are parallel. Therefore, by the Triangle Proportionality Theorem, Substitute the values and solve for x. Cross multiply. 6x = 18 Divide both sides by 6. The value of x is 3.

  9. Example 5 • Solve for x.

  10. Example 6 • Solve for x.

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