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 and E 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. If AD = 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 XY is 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. 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. EXAMPLE 4 Find the value of x.

9. EXAMPLE 5  Solve for x.

10. EXAMPLE 6  Solve for x.