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. Which statement can be proved true using the given theorem?

Answer 1

Which statement can be proved true using the given theorem?

Segment BF = 16

Segment BD = 20

Segment BD = 15

Segment BF = 32

Answer 2

i think its Segment BD=15 but im not sure

Answer 3

can someone please help me?

Answer 4

segment BF = 36 as the ratio of the small triangle to the big triangle is 5:11

Answer 5

small triangle in this case is EFC, large triangle is ABC

Answer 6

ok so BF=16 right?

Answer 7

since its the smaller one?

Answer 8

...no, BF = 36

Answer 9

okay, but thats not one of my options.

Answer 10

the line BC = 66 and the segment FC = 30, so the segment BF = 36

Answer 11

so that's eliminated 2 possible answers, now we focus on the line BD

Answer 12

ok so since BF= 36 now we need to find BD right?

Answer 13

i believe the answer is BD=15 but im not completly sure?

Answer 14

so as it's a parallelogram, the line EF = line BD

Answer 15

so should we use pathogoream theroem to find EF?

Answer 16

sorry dude, wifi dropped out for a sec

Answer 17

oh its okay thanks for coming back

Answer 18

back now
no just use the ratio, it's easier
if BD = 20, then AB = 38
so is that a 5:11 ratio?

Answer 19

yes

Answer 20

no, a 5: 11 ratio on 20 would be a side length of 44 for AB

Answer 21

oh yeah true that

Answer 22

so the answer is bd=20 right?

Answer 23

so we'll try the 15
15 + 18 gives us a length AB of 33
and a 5: 11 ratio of 15 gives us:
15/5 = 3 x 11 = 33
matches
success, answer's segment BD = 15

Answer 24

oh so i was right from the start? ha

Answer 25

yep, props, but now you can prove why

Answer 26

yes thank you alot i dont know if you could maybe help me on some other problems ill post them

Answer 27

sure dude, shoot

Answer 28

okshould i post them in the chat or new post?

Answer 29

nah keep it going here is fine

Answer 30

ok cool one sec

Answer 31

Hillary is using the figure shown below to prove Pythagorean Theorem using triangle similarity.

In the given triangle ABC, angle A is 90o and segment AD is perpendicular to segment BC.

Answer 32

Which of these could be a step to prove that BC2= AB2 + AC2?

Segment AD : segment CD = segment BD : segment AD, since triangle ADB is similar to triangle CDA.

Segment AC : segment DA = segment BC : segment AC, since triangle ABC is similar to triangle DAC.

Segment BC : segment AC = segment AC : segment DC, since triangle ABC is similar to triangle DAC.

Segment BD : segment BA = segment BA : segment CA, since triangle ADB is similar to triangle CDA.

Answer 33

i thought it was choice 3 can you check if im right?

Answer 34

am i right?

Answer 35

so what im getting is that the similar triangles are ABC is to DAC
so line DA (small tri) is some ratio of AB,
line AC (small Tri) is the hypotenuse, similar to BC
which leaves DC (small tri), the smallest side, a ratio of AC

Answer 36

yeah man, looks like you're spot on there with option 3

Answer 37

lets go im on a roll! next question?

Answer 38

shoot, but last one, i got a couple of my own i need to post for an assignment

Answer 39

ok last one its kind of long though you think yyou can help me?

Answer 40

yeah, lets do it

Answer 41

awesome ok one sec

Answer 42

The figure below shows a kite labeled PQRS.

Answer 43

Write a 2-column, paragraph, or flow-chart proof to show that vertex angles of a kite are bisected by the diagonal.

Answer 44

this one i have no idea how to do it, so ima need your help big time. can you give me like all the steps?

Answer 45

hmm tell me what a vertex angle is first?

Answer 46

angle formed by 2 legs?

Answer 47

and i thought a diagonal was a line going across... this may sound stupid, but diagonally

Answer 48

ok, so the angle at P and the angle at R... yeah?

Answer 49

yes

Answer 50

that's easy enough then
any quadrilateral (4 sided figure) will have 4 angles that will each be less than 180 degrees, and all 4 will always add up to 360 degrees, in the same way that any triangle is made up of 3 angles, each will be less than 180 degrees and the sum of them will always be 180 degrees

Answer 51

so what are the steps i would need to prove it?

Answer 52

so provided the length of side PQ = PS and RQ = RS, then angle Q must = angle S

Answer 53

thats the given?

Answer 54

it has to be assumed, as it's the only way the vertical line could equally bisect the angles P and R

Answer 55

ok, sounds good, hey jack, do you possibly think you could right the paragraph proof for me? its my last question and test has to be in soon.

Answer 56

its usually denoted by these symbols, the lines with the single dash through them are the same length as other lines with a single dash through them, and same goes for lines with double dashes = length of other lines with double dashes

Answer 57

ok.

Answer 58

so how can i write the paragraph proof?

Answer 59

thank you for helping me by the way your very helpful :)

Answer 60

flow chart proof
length PQ = Length PS
and
lenght RQ = length RS
therefore
angle Q = angle S
therefore as line RP is same length in both triangle PQR as for PSR
and angle Q = angle S
and Side PQ = Side PS
and Side RQ = Side RS
you have 2 triangles with exactly the same dimensions, 3 equal sides, and one known equal angle

Answer 61

which means that angle P and angle R must be perfectly bisected by line RP, or else you wouldn't have equal dimensions in your triangle side lengths

Answer 62

thats the whole answer? for the flow proof chart?

Answer 63

yes... providing they're mirrored triangles (PQ = PS = true)
if not then they're reflected triangles, and the angle of the LH triangle at P = angle of the RH triangle at R, and vice versa

Answer 64

ok thanks im going to put all this info in my own words. thanks alot

Answer 65

sweet, good luck dude