Given: df and de are midsegments of abc prove: de=1/2 ac

Solution-

Given, DF and DE are midsegments of ABC. so D is the mid point of AB and F is the mid point of AC.

Considering AB,

Then DE is parallel to AC, as mid-segments are parallel to the non included side of the triangle.

Also, according to corresponding angle theorem,

Then,

As,

According to similarity of two triangles,

step-by-step explanation:

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a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional