Question

Look at the figure.



Make a two-column proof showing statements and reasons to prove that triangle NMT is similar to triangle NMP.

Answer 1

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1008_13/image0034e8cadde.jpg

Answer 2

the one reason of being similar is the same angle of 50*.

Answer 3

P.S. I'm not sure.

Answer 4

yes, AND the share a common angle.... so that means the third angle has to be the same...
therefore you have AAA similarity....:)

Answer 5

*they share

Answer 6

So how would I make a two-column proof out of that? What would it look like?

Answer 7

i think it's saif to say that it's AAA similarity....:)

Answer 8

Statements Reasons
???????? ???????

Answer 9

I always sucked at proves, unfortunately. :(

Answer 10

@dpaInc are you good with proofs?

Answer 11

we basically gave the proof to you... just mention what we said in a two column proof way...
start with the given... then the next statement should be the common angle (reason is reflexive property), third, is the fact that if two angles between two triangles are the same then the third one has to be the same since all triangles add up to 180 degrees...

Answer 12

I don't really understand how to put the second part in a proof?

Answer 13

Statements Reasons
Angle TNM is equal to 50 Given
Angle NPT is equal to 50

Answer 14

@nbouscal

Answer 15

I would say that angle TNM is equal to angle NPT, given, and that angle NMT is equal to NMP, because reflexive property, and then that angle NTM is equal to angle PNT because the angles have to add to 180, so they are congruent because AAA.

Answer 16

Statements Reasons
Angle TNM=angle NPT Given
Angle NMT=angle NMP Reflexive Property
Angle NTM=angle PNT Angles add up to 180 degrees
Triangle NMT=triangle NMP AAA

Does that look right?

Answer 17

ok... basically nathan gave u the proof in paragraph form..., i think it would help you more if you just rewrite exactly what he said but in two-column form....
start with the given....
angle so and so are both 50 reason: given

do the rest....

Answer 18

@dpaInc did the proof I just typed in look right to you?

Answer 19

sure.... but be more specific in your reason for the third statement.... "all three angles in any triangle add up to 180"

Answer 20

Thank you so much!

Answer 21

yw..:)