Question

Theorem: A line parallel to one side of a triangle divides the other two proportionately.

In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB.

The figure shows triangle ABC with segments DE and EF. Point D is on side AB, point E is on side AC and point F is on side BC. Segment AD is 6, segment AE is 12, segment EC is 18, and segment FC is 24

Which statement can be proved true using the given theorem?

Segment BD = 12

Segment BD = 4

Segment BF = 16

Segment BF = 9

Answer 1

@ganeshie8 how do i set up the proprtions?

Answer 2

look at options, they involve two lengths : BD and BF

Answer 3

so, lets find them both

Answer 4

okay

Answer 5

yes we need to setup proportions :)

Answer 6

how? :p

Answer 7

lets find BD first ?

Answer 8

okay

Answer 9

look at the other side, we have 12 and 18 there

Answer 10

on left side, we have 6 and BD

Answer 11

oh! so it would be 6/BD = 12/18?

Answer 12

thats it !

Answer 13

which equals 9!!

Answer 14

correct ! so strike off first two options

Answer 15

lets find BF also

Answer 16

BF equals 12...

Answer 17

careful...

Answer 18

not 12?

Answer 19

we have 24 and BF on onse side
the other side we have 18 and 12

Answer 20

16 :) i multiplied wrong oops

Answer 21

Excellent !

Answer 22

yay!

Answer 23

good work :)

Answer 24

you too :)