Question

Hi ( : can some one explain how to make a two column proof for the triangle below to prove that triangle PQR is similar to triangle PQS?

Answer 1

Would I start by stating that m<PQS = M<PRQ?

Answer 2

@jim_thompson5910 Hi (: can you help me with this?

Answer 3

That is one good way to start. That's how I would start. Why is m<PQS = m<PRQ true?

Answer 4

It's given that they are both 30*

Answer 5

good, the reason is simply "given"

Answer 6

what else do you need to prove that triangle PQR is similar to triangle PQS

Answer 7

They both share side PQ by the reflexive property

Answer 8

that is true, but not really useful for this case

Answer 9

what else do they share?

Answer 10

Oh, the interior angles add up to 180*?

Answer 11

that's true for all triangles

useful information...yet not handy in this proof really

Answer 12

you pointed out that PQ was shared, is anything else shared?

Answer 13

PS is part of PR

Answer 14

that's also true, but I'm leaning more towards angles (instead of side lengths)

Answer 15

what angles are shared?

Answer 16

oh! <P

Answer 17

good, angle P is shared, so you can use this idea to say that < P = < P (reflexive property)

Answer 18

what's your last step?

Answer 19

triangle PRQ is similar to triangle PSQ by the AA similarity theorem

Answer 20

you nailed it

Answer 21

very nice job

Answer 22

Thank you! :D

Answer 23

you're welcome