Question

Look at the figure.



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

Answer 1

I'm clueless where to start lol

Answer 2

First set up a two column proof, then if you have speific questions, ask.

Answer 3

They share angle P. They both have a 30 degree angle. So looks like they must be similar by AA similarity. Now all you have to do is put in in 2 column form with statements and reasons.

Answer 4

Do you know what similar triangles are?

Answer 5

yes I do

Answer 6

That's a good start. Do you know what you need to show to prove that two triangles are similar?

Answer 7

Would this be a good two column proof?

They Share Angle P -- Construction
They both have a 30 degree angle -- Construction
They are similar because of angle P and the two 30 degree angles -- AA similarity.

Answer 8

@Mertsj

Answer 9

You're on the right track.

Answer 10

First set up the proof with two columns. Write "Statements" over the left columnm, and "Reasons" over the right column.

Answer 11

Ok I can add those over the two columns

Answer 12

Statements | Reasons
1. <P is congr. to <P | 1. Reflexive prop of congruence

Answer 13

That states that <P is congr. to itself.
Now you need to state the other two angles that are congruent.

Answer 14

Statements | Reasons
1. <P is congr. to <P | 1. Reflexive prop of congruence
2. <R is congr. to <PQS | 2. Given

Answer 15

Since you have two angles of one triangle congruent to two angles of another triangle, then by AA Similarity, the triangles are similar. This is what you wrote above. That's your next statement.

Answer 16

Statements | Reasons
1. <P is congr. to <P | 1. Reflexive prop of congruence
2. <R is congr. to <PQS | 2. Given
3. tr PRQ ~ tr PQS. | 3. AA Similarity

Answer 17

Thanks!

Answer 18

You're welcome. This was a simple proof, and you came up with the strategy. Good job!