Question

Carla drew two triangles; triangle ABC and triangle PQR, on a grid. She planned to cut out the two triangles to make a flag. The vertices of triangle ABC are at A(1, 4), B(-2, -1), and C(3, -2). The vertices of triangle PQR are at P(-3, 0), Q(-2, -4), and R(2, 3).

Using the coordinates of the vertices of each triangle explain whether the two triangles are congruent, similar or neither.

Give me a sec and I will graph this

Answer 1

There they are sketched out.

Answer 2

They don't look congruent or similar.

Answer 3

One is a right triangle and the other looks obtuse

Answer 4

@apoorvk

Answer 5

None of the dimensions are evenly distributed between the 2 triangles either.

Answer 6

Great, okay!
Now we don't go by looks in such cases, looks can be deceptive :P
So what we need to do her is that, we find out all the sides of the 2 triangles, that is you will need to use the distance formula 6 times.

And then, is all 3 pair of sides are equal, then they are congruent, if the ratios of side-lengths are constant and equal then they are similar triangles!

And. If none - then none. -_-

Answer 7

What is the distance formula?

Answer 8

Hmm
For two points, say A(x\(_1\),y\(_1\)) and B(x\(_2\),y\(_2\)), the distance AB between them is:
\[AB = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\]

Any old memories resurfacing? :P

Answer 9

ohhhh yeah. Damn. Do I have to do that 6 times D:

Answer 10

gr I have to get up and get a pen and paper and turn my light on xD

Answer 11

i think they are neither congruent nor similar. the ratios AB/PQ and BC/QR are not equal.

Answer 12

Alright here goes nothing (everything) xD

1. (1,4)(-3,0)
= (-2, -4)
2. (-2,-1)(-2,-4)
= (-4,-5)
3. (3,-2)(2,3)
= (1,-5)

(-2,-4)(-4,-5)(1,-5)

Did I do that right?

Answer 13

I don't think I did. Damn it. Dx

Answer 14

yea, u didn't. use the distance formula apoorvk showed above. and find out the lengths of any 2 corresponding sides. and then take their ratio.
like, i found out AB and BC in triangle ABC and PQ and QR in triangle PQR. and then i took the ratio of the corr sides: AB/PQ and BC/QR.

Answer 15

I"m screwing something up...Idk what though
like the first set for example
(1,4) (-3,0)

-2^2 + -4^2 = 4 + 16 = 20 or something. idk D: Can one of you help me with just one of them and I can do the rest I swear.

Answer 16

okay. lets find out AB first, then.
A = (1,4)
B = (-2,-1)
so AB = \[\sqrt{(1 + 2)^{2} + (4+1)^{2}}\]
\[= \sqrt{3^{2} + 5^{2}}\]
\[= \sqrt{9+25}\]
\[= \sqrt{34}\]
\[= 5.83\]

Answer 17

Okay! Thank you so much! Give me a few minutes for this

Answer 18

sure, take ur time!

Answer 19

Okay and I have:
(1,4)(-2,-1) = √34 = 5.83
(-2,-1)(3,-2) = √34 = 5.83
(1,4)(3,-2) = √8 = 2.82


(-3,0)(-2,-4) = √51 = 7.14
(-2,-4)(2,3) = √65 = 8.06
(-3,0)(2,3) = √34 = 5.83


Is this good?

Answer 20

Oh wait, (-3,0)(-2,-4) = √41 = 6.4

Answer 21

(-2,-1)(3,-2) = √34 = 5.83 <=..........this should be sqrt(26) not of 34. i didn't confirm the others yet. but, u'd better re-check ur calculations.

Answer 22

Is (1,4)(3,-2) = √40 = 6.32?

Answer 23

yup. that's right.

Answer 24

(1,4)(-2,-1) = √34 = 5.83
(-2,-1)(3,-2) = √26 = 5.1
(1,4)(3,-2) = √40 = 6.32

(-3,0)(-2,-4) = √41 = 6.4
(-2,-4)(2,3) = √65 = 8.06
(-3,0)(2,3) = √34 = 5.83


Okay. I think I got it. :D

Answer 25

that's great! now just take any 2 ratios and see if their values match.

Answer 26

ratios of corresponding sides, though!

Answer 27

Well the very first and last ones do, I think? Or are those just angles?

Answer 28

i didn't get u. u mean 5.83/6.4 and 6.32/5.83?

Answer 29

I thought the 5.83 stand by themselves? I didn't know they become fractions :/

Answer 30

I think AC and PR are similar?

Answer 31

see, 2 triangles are similar if the ratios of their corresponding sides are equal. and they are congruent if their 'corresponding' sides are equal. here, we can clearly see that the latter is not the case. so we're seeing if they are similar by taking the ratios. got it?

Answer 32

Okay, I think so. I'm pretty sure I do. The only similar sides are AC and PR, I think

Answer 33

when u're testing the similarity between 2 triangles, u always take sides in pairs. so u can't have AC = PR and hence the 2 triangles are similar. as i said abv, take the ratio of corr sides. ie, AB-PQ, BC-QR, AC-PR. and check if these 3 ratios are equal or not.

Answer 34

no.no.yes. ? so it is neither similar nor congruent?

Answer 35

the answer should be just no. where did that yes come from?

Answer 36

and yes, its neither similar nor congruent.

Answer 37

oh .-. I'm really sorry if I'm frustrating! If I could give you like 100 medals I would. Thank you so much for helping me!

Answer 38

lol! don't worry! i'm happy i could help u out! i hope u understood this and will be able to solve similar kinds in future. :)

Answer 39

Thank you, thank you, thank you! (I can finally go to bed now :D) lol

Answer 40

lol! kk...g'night!

Answer 41

Night! :D