Question

http://prntscr.com/a8s6h5
So, I understand all but one of the steps. Could someone explain why in step six the denominator's are RQ and SQ? Like, what property of equality makes step six make sense?

Answer 1

@jhonyy9 Can you help me with mine?

Answer 2

step 6 cam from step 4 with the substitutions made using step 5...
you already know how step 4 came and how RQ and SQ are already the denominators, right?

Answer 3

Hm, I don't think I explained this properly. I know where the step came from. I want to know what property of equality justifies step six. For eg, why in step 6 did it go froom the equal sign (=) to the division sign XR+RQ/RQ and why did RQ and YQ replace XQ and YQ?

Answer 4

@imqwerty

Answer 5

@imqwerty HALP this poor fellow

Answer 6

@ganeshie8

Answer 7

Does step4 make sense to you ?

Answer 8

Yes.
@ganeshie8

Answer 9

Do you see how XQ equals XR+RQ ?

Answer 10

Yes, What I don't understand is why after step 5 the equation went from XQ=XR+RQ and YQ=YS+SQ to a proportion equation where XR+RQ/RQ=YS+SQ/SQ. Where did that equation come from? How did that translation come from?
@ganeshie8

Answer 11

Forget about step5

Stare at step4 and step6 a bit

Answer 12

they are taking the equation from step4 and replacing the numerators in step6

Answer 13

@ganeshie8
Explain step four to me then. Maybe I'm misunderstanding it.

Answer 14

How many triangles do you see in the given diagram ?

Answer 15

Two
@ganeshie8

Answer 16

Are they similar ?

Answer 17

Yes
@ganeshie8

Answer 18

So the corresponding sides form a proportion

Answer 19

XQ and RQ are corresponding sides

YQ and SQ are corresponding sides

Answer 20

\[\dfrac{XQ}{RQ} = \dfrac{YQ}{SQ}\]

Answer 21

Alright. I understand so far.
@ganeshie8

Answer 22

Take above equation and replace the numerators

Answer 23

replace \(XQ\) by \(XR+RQ\)

Answer 24

replace \(YQ\) by \(YS + SQ\)

Answer 25

What step is that? Also, I understand.
@ganeshie8

Answer 26

Step6

Answer 27

Ah, alright. Can you explain the last step?
@ganeshie8

Answer 28

Take step6 :
\[\dfrac{XR+RQ}{RQ} = \dfrac{YS+SQ}{SQ}\]

Answer 29

distribute the denominator :

\[\dfrac{XR}{RQ}+\dfrac{RQ}{RQ} = \dfrac{YS}{SQ}+\dfrac{SQ}{SQ}\]

Answer 30

\[\dfrac{XR}{RQ}+1 = \dfrac{YS}{SQ}+1\]

Answer 31

cancel 1 both sides and get

\[\dfrac{XR}{RQ} = \dfrac{YS}{SQ}\]

which is the last step

Answer 32

In your proof, they did not show all that simplification

Answer 33

THANK YOU
@ganeshie8

Answer 34

Yw