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|dw:1347551396246:dw|

What are the blanks? If you don't mind me asking.

4th row we need to fill

so lets see whats happening in the next row - 5th one

4th and 6th

yea in 5th row, we are using AA similarity.
which means we need two congruent Angles ?

Okay

did u understand 3rd row ?

Not really, I'm not good with Postulates.

|dw:1347552555431:dw|

look at the pix,
DE is parallel to AC, its given

Yes, I understand that.

now lets do some imagination

Alright

think, you slide the side AC up and put it over DE

|dw:1347552973501:dw|

Got it.

then, since both lines are parallel,
if you shrink AC,
A overlaps wid D and C overlaps with E

right ?

Yes

since two sets of corresponding angles are equal,
both triangles, small and big ones, are similar

Yes

|dw:1347553320251:dw|

so 4th statement can we have like this :
< BED \(\cong\)

Agreed

|dw:1347553430140:dw|

good lets think of last row

Okay

last row must contain the thing asked for proving

Prove: BD over BA equals BE over BC

yea so lets put the last statement as
\( \frac{BD}{BA} = \frac{BE}{BC} \)

can you think of what will be the Reason/justification ?

Um to be honest I have no idea...........Like I said I'm horrible at justifications.

So the answer is BDBA=BEBC "Corresponding sides of similar triangles are proportional"?