Question

My class is working with SSS and SAS, I was wondering if somebody could help me with two of my proofs? They are in the comments section.

Answer 1

Show that the triangles are congruent for the given value of the variable.

Answer 2

\[\triangle GHI \cong \triangle IHJ, x=4\]

Answer 3

hmmm that your given \(\triangle GHI \cong \triangle IHJ\) does not seem right

Answer 4

No, they want me to prove that.

Answer 5

well it can't be if your diagram is correct

Answer 6

you mean \(\triangle GHJ\cong\triangle IHG\)

Answer 7

Oh, yeah. Sorry.

Answer 8

Okay so
x=4 you say

Answer 9

Yes, and I need to use that to write a two-column proof showing that the triangles are congruent.

Answer 10

if x=4 then 2x-9=3
and 2x-3=5
that means \(HG\cong HI\) and \(GJ\cong IJ\)

Answer 11

now we also have HJ is a common segment
then by SSS the two triangles are congruent

Answer 12

that's the proof

Answer 13

Ok, got it thank you.

Answer 14

welcome

Answer 15

@Directrix could you help me with this one.

They give x=4
They want me to prove \[\triangle RST \cong \triangle TUR\]

Answer 16

My bad looking at the last one x=18

Answer 17

eh it's the same thing
now they want you to do SAS

Answer 18

Yes, they gave me x=18.

Answer 19

4x-11=61
2x=36
what does mean

Answer 20

UT=RS
and \(\angle RTU\cong \angle TRS\)

Answer 21

4(18)-11=61 - RS=UT
2(18)=36 - \[\angle RTU \cong \angle TRS\]

Answer 22

you need one more side to have SAS can you figure it out

Answer 23

No it is not given to be a parallelogram @Directix, sorry wasn't trying to ignore you, just trying to keep up with both of you. I do not know how to get the other sides, that is why I'm so confused @xapproachesinfinity

Answer 24

hmmm lol
@Directrix we can't assume it is a quadrilateral
we one to prove that by proving that the two triangle are congruent

Answer 25

well again there is a common side btw the two triangle

Answer 26

so by sas they are indeed congruent

Answer 27

Oh, gosh I am always over thinking things, I kept ignoring that side and wanted to try proving RU=ST. LOL

Answer 28

hmm... you need to get an easier way always if it is available

Answer 29

>>> we can't assume it is a quadrilateral we one to prove that by proving that the two triangle are congruent

FALSE

Answer 30

this is a two column proof so no need to go further proving a hard side

Answer 31

Thank you both for helping me, I have to go now. Dinner is ready.

Answer 32

of course we still need more to prove it is quadrilateral our concern here
is jut the concurrency of the two triangles

Answer 33

YW!