Question

Could someone please help me out with this one.?
Make a two-column proof showing statements and reasons to prove that triangle PRQ is similar to triangle PQS.

Answer 1

well for starters, we know that

angle PRQ = angle PQS

since both are 30 degrees

Answer 2

also, we know that

angle RPQ = angle SPQ

because they are common angles (they overlap and are basically the same)

Answer 3

so that's enough info to say

triangle PRQ ~ triangle PQS

by the AA similarity theorem

Answer 4

overlap..? srry. Could u explain that..?

Answer 5

AA = angle angle

Answer 6

let me try a drawing

Answer 7

okee thank you :))

Answer 8

we're given this

Answer 9

we know these two angles are congruent



because they're both 30 degrees

Answer 10

this angle here

Answer 11

angle RPQ

is congruent to this angle here (SPQ)

Answer 12

alright. yeah. because they both have the P as the angle so it would be the same degree..right? lol :DD

Answer 13

exactly

Answer 14

yay!! thank youu!! :DD

Answer 15

so we know that

angle PQS = angle PRQ

angle RPQ = angle SPQ

Answer 16

so how would i start a two column proof with that? I know to have the Given included.

Answer 17

these two facts are used to say

triangle PRQ ~ triangle PQS by the AA similarity theorem

Answer 18

the first two are given (given to be 30 degrees)

the next two are common angles (common angles overlap perfectly...so they must be the same angle)