The table shows the proof of the relationship between the slopes of two perpendicular lines. What is the missing statement in step 2?

- anonymous

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- anonymous

1.
is similar to .
given
2. property of similar triangles
3. = property of proportion
4. slope of =
slope of = definition of slope
5. slope of × slope of = multiplying the slopes
6. (This statement is intentionally left blank.) Substitution Property of Equality
7. slope of × slope of = -1 simplifying the right side

- anonymous

couldnt get all of it but tried my best

- jim_thompson5910

a screenshot is best because we can see the full problem (even the missing symbols)

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## More answers

- anonymous

1. AC←→⊥CD←→ (view diagram)
ΔABC is similar to ΔCED. given
2. (This statement is intentionally left blank.) property of similar triangles
3. ABBC = ECDE property of proportion
4. slope of AC←→ = -ABBC
slope of DC←→ = DEAC definition of slope
5. slope of AC←→ × slope of DC←→ = -ABBC×DEEC multiplying the slopes
6. Substitution Property of Equality
7. slope of AC←→ × slope of DC←→ = -1 simplifying the right side

- anonymous

sorry here it is

- jim_thompson5910

well step 3 has AB*BC = EC*DE, or so it seems
the step before that would be some proportion and cross multiplying would lead to step 3

- jim_thompson5910

does that make sense?

- anonymous

not really but u can explain it in detail. mabye ill get it

- jim_thompson5910

let's say you had
a/b = c/d

- jim_thompson5910

if you cross multiplied, you'd get a*d = b*c
agreed?

- anonymous

yea

- jim_thompson5910

so what proportion could be set up to lead to AB*BC = EC*DE ?

- anonymous

they seem to look like this but in fraction AB/BC;. something like that.

- anonymous

AB/DE, and EC/DE

- jim_thompson5910

more like AB/EC = DE/BC. There are other possibilities
|dw:1436929680423:dw|

- jim_thompson5910

|dw:1436929728958:dw|

- anonymous

oops sorry. thats not on my answer choices tho

- anonymous

the closest choice has a fraction DE/EC. would that work?

- jim_thompson5910

well as long as they cross multiply to AB*BC = EC*DE, then it will work

- jim_thompson5910

there are more possibilities than what I drew up there (maybe 4 possibilities?)

- anonymous

ok hold on

- anonymous

AB/EC=BC/DE
AB/BC=DE/EC
AB=DE BC=EC
AB/BC= -EC/DE

- anonymous

##### 1 Attachment

- jim_thompson5910

choice C looks funky...there are no fractions there?

- jim_thompson5910

try posting a screenshot if you can

- anonymous

there are no fractions in c, and sorry i cant post a screenshot.

- jim_thompson5910

ok let me think

- jim_thompson5910

in line 3, where it says `3. ABBC = ECDE property of proportion` there are no fractions here either?

- anonymous

actually yea those are fractions

- anonymous

its really hard to paste those kinds of things on here.

- jim_thompson5910

so line 3 actually says this right?
AB/BC = EC/DE

- anonymous

yes yes

- jim_thompson5910

|dw:1436930874242:dw|

- jim_thompson5910

you can multiply both sides by BC and divide both sides by EC
that will make BC and EC swap
|dw:1436930925056:dw|

- jim_thompson5910

giving
|dw:1436930949685:dw|

- anonymous

omg thanks so much!

- anonymous

can you help me with one more? its a mastery, and i didnt really understand this lesson

- jim_thompson5910

sure

- anonymous

AB and BC form a right angle at point B. If A = (-3, -1) and B = (4, 4), what is the equation of BC

- jim_thompson5910

first find the equation of the line through A and B

- anonymous

slope?

- anonymous

5/7 is the slope

- jim_thompson5910

use that slope to find the equation of the line through those two points

- jim_thompson5910

you can use y = mx+b

- anonymous

i think its y=5/7x+8/7

- jim_thompson5910

yep

- jim_thompson5910

|dw:1436931657035:dw|

- jim_thompson5910

AB and BC form a right angle, so
|dw:1436931712083:dw|

- jim_thompson5910

what is the slope of BC ?

- anonymous

x + 3y = 16
2x + y = 12
-7x − 5y = -48
7x − 5y = 48

- anonymous

these are the answer choices btw. and the slope for BC is -7/5 right?

- jim_thompson5910

what is the equation of the line going through B and has slope of -7/5

- jim_thompson5910

use y = mx+b

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