Question

Which of the following statements is true only if triangles EFI and GFH are similar?

A. 2FI = 3FH
B. Lines EI and HG are parallel
C. Points E, F, and G are collinear
D. EI / FI = GH / FH

Answer 1

What do you think?

Answer 2

dont know

Answer 3

A maybe

Answer 4

Can you test each option?

Answer 5

how do i do that?

Answer 6

uh yea how do you do that

Answer 7

Start with easy ones, B and C.

Answer 8

i guess cross those out

Answer 9

B. Lines EI and HG are parallel
Are they parallel?

Answer 10

no

Answer 11

no

Answer 12

C. Points E, F, and G are collinear
Are they on same line?

Answer 13

no

Answer 14

no

Answer 15

Both B and C are correct. The segments are parallel and the 3 points are collinear... But it doesn't come from the similarity of the triangles.

Answer 16

wait wym? theres only one correct option...

Answer 17

What property do you know about similar triangles that can help to chose the only correct answer?

Answer 18

you mean, AAA, SAS, and SSS?

Answer 19

The ratio of corresponding sides is same.

Answer 20

You need to chose between A and D based on this property

Answer 21

ohh

Answer 22

since you said ratios, its D, right?

Answer 23

Can you confirm if this is the ratio of corresponding sides?

Answer 24

no? i dont know how to do that..

Answer 25

Can you match the corresponding sides of the two triangles?

Answer 26

For example, EI and HG are corresponding sides

Answer 27

i dont understand.. sorry, can you explain it little bit more?

Answer 28

The two triangles are similar, it means one of them is smaller copy of the other. Let one has sides 3, 4 and 5 and the other has sides 6, 8 and 10.
Then 3 and 6 are corresponding as well as 4 and 8 or 5 and 10.

Answer 29

You get same ratio when divide the matching sides:
6/3 = 2
8/4 = 2
10/5 = 2

Answer 30

This is the ratio of corresponding sides

Answer 31

ohhh, i understand now, tysm

Answer 32

Great. Now, can you list the sides of the bigger triangle?

Answer 33

do you mean this...?

3/6 = 1/2
4/8 = 1/2
10/5 = 1/2

Answer 34

No, the one in the picture

Answer 35

what?? im confused again :')

Answer 36

same

Answer 37

EFI is the bigger triangle
And its sides are:
EF, FI and EI, right?

Answer 38

ohhh, you wanted me to name the sides... im dumb 🤦 alright...

EF, FI and EI
FH, FG, and HG

Answer 39

No problem, its fine. I should have mentioned...
Fine, can you tell which sides are matching between bigger and smaller triangles?

Answer 40

I already mentioned one above

Answer 41

EI and HG
EF and FH or FG?

Answer 42

EF and FG. And the last pair is?

Answer 43

FI and FH

Answer 44

If you divide each pair, you should get same number. Can you show this?

Answer 45

yea, thats what we just did, right?

Answer 46

If the ratio is k, then it is:
EI /HG = k
EF /FG = k
FI /FH = k

Answer 47

Now ignore the middle one and make the others same

Answer 48

EI/HG = FI/FH

Answer 49

Can this be converted into the option D?

Answer 50

yea, i think so

Answer 51

So you have the answer now

Answer 52

thank youuuu<3

Answer 53

No problem. Have a good time!