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.