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
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
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.
EXAMPLE 2
Given DE is the length of the mid-segment. Find AB.
Solution: AB = 16m
EXAMPLE 3
Given XY is the length of the mid-segment. Solve for x.
Solution: ½ (18) = (2x-6)9 = 2x – 615 = 2x7.5 = x
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
The lines are parallel. Therefore, by the Triangle Proportionality Theorem,
Substitute the values and solve for x.
Cross multiply.6x = 18Divide both sides by 6. The value of x is 3.
EXAMPLE 4
Find the value of x.
EXAMPLE 5
Solve for x.
EXAMPLE 6
Solve for x.
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