Question

@jim_thompson5910
I'm stuck between B and D ! :(

Answer 1

this sort of thing involves a lot of drawings and it can get very messy

hopefully this page makes things simple (or at least less complicated)

http://www.math.nmsu.edu/~breakingaway/Lessons/PTUST/PTUST.html

let me know if that page helps or not

Answer 2

Confused..

Answer 3

where at?

Answer 4

divisions on bottom

Answer 5

you mean like the c in a/c ?

Answer 6

yes

Answer 7

do you see how c is the hypotenuse of the largest triangle?

Answer 8

yes

Answer 9

also notice how they isolated triangle 1 and triangle 2

Answer 10

they drew them below the largest triangle

Answer 11

for triangle 1, a is the hypotenuse
for the largest triangle, c is the hypotenuse

they correspond which means a/c

-------------------------------------------------------

at the same time,
for triangle 1, x is the short leg
for the largest triangle, a is the short leg

they correspond ---> x/a

-------------------------------------------------------

the two ratios are equal which is how they got

a/c = x/a

Answer 12

make sense?

Answer 13

okay

Answer 14

they use a similar approach to get

b/c = y/b

make sure you understand how they got that

Answer 15

be sure to focus on triangle 2 and the largest triangle

Answer 16

>.<

Answer 17

still stuck?

Answer 18

yes

Answer 19

focus on triangle 2 and the largest triangle

for triangle 2, what is b? hypotenuse? short leg? long leg?

Answer 20

b is the long leg
I went back and re-read your response. Yes, it makes sense.

Answer 21

b isn't the long leg for triangle 2

Answer 22

notice how it's opposite the 90 degree angle

Answer 23

where is the 90 degree angle?

Answer 24

it's where segment h and segment y meet

Answer 25

?

Answer 26

yes that is correct

Answer 27

those angles you marked are all 90 degrees

Answer 28

for triangle 2, b is opposite the 90 degree angle, so b is actually the hypotenuse

longest side is always opposite largest angle

Answer 29

Yahooo! :)
It makes a bit more sense with the 90 degree angles marked.

Answer 30

sorry I had them flipped, but here it's fixed

Answer 31

based off that, we see that

triangle ADB ~ triangle CDA (look at triangle 1 & 2, notice how they match up)

Answer 32

we also see that

triangle BCA ~ triangle BAD (focus on larger triangle and triangle 1)

Answer 33

Okay...

Answer 34

so were you able to get any further based on that?

Answer 35

I think it's B.

Answer 36

why is that?

Answer 37

A =D

Answer 38

I don't know what you mean

Answer 39

how are A and D equal?

Answer 40

A=D
oh crap but C is also equivalent to A.. -_-

Answer 41

do you see how

triangle ADB ~ triangle CDA
and
triangle BCA ~ triangle BAD

??

Answer 42

yeah.

Answer 43

I'm going to call the overall largest triangle, triangle 3

triangles 1 and 2 are below triangle 3

Answer 44

triangle ADB and triangle CDA are what two triangles?

(use labels triangle 1, triangle 2 or triangle 3)

Answer 45

triangle ADB is _______

fill in the blank with triangle 1, triangle 2 or triangle 3 (look at how I labeled triangle ADB)

Answer 46

1

Answer 47

correct

Answer 48

DAC is 2

Answer 49

triangle CDA is triangle 2, yes

Answer 50

think back to this page

http://www.math.nmsu.edu/~breakingaway/Lessons/PTUST/PTUST.html

notice how they connect


triangle 1 with triangle 3 (to get a/c = x/a)
and
triangle 2 with triangle 3 (to get b/c = y/b)

Answer 51

they do NOT connect triangle 1 with triangle 2

Answer 52

so triangle ADB ~ triangle CDA is definitely true, but it's not relevant or used here

Answer 53

that allows us to eliminate the first two answer choices

Answer 54

make sense?

Answer 55

Y E S : D

Answer 56

let's look at choice D

does BA correspond to DA (look at triangle 3 and triangle 1) ?

Answer 57

no

Answer 58

BA corresponds to BD instead, so choice D is also eliminated

Answer 59

Ah, it is C.

Answer 60

:D !!

Answer 61

correct

Answer 62

Thank you!!

Answer 63

np