Question

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

Answer 1

@phi

Answer 2

Just like there is ASA, SAS, SSS, etc. for proving triangles congruent, are you familiar with a way of proving triangles similar?

Answer 3

not really @mathstudent55

Answer 4

@ganeshie8

Answer 5

@Destinymasha

Answer 6

@countonme123

Answer 7

@poopsiedoodle

Answer 8

Oh geez. I'd help, but I'm horrible with proofs. @mathmale maybe?

Answer 9

@poopsiedoodle thanks

Answer 10

@mathmale please help me

Answer 11

to show two triangles are similar, show that corresponding angles are congruent (equal)
because all 3 angles of a triangle add up to 180 degrees,

Notice that if you know 2 of the angles in a triangle then you know the 3rd one (because all 3 angles add up to 180. the third angle will be 180 - (sum of the other two))

They tell you there is an angle in both triangles = 30
what you need is to show a second angle in both triangles are equal to each other.
(and then the third angles must also be equal) and you are done.

Answer 12

To show two triangles are similar, you can use "AA Similarity".
To do that, all you need to do is show that two angles of one triangle are congruent to two angles of the other triangle.

Look at the triangles you were given.

They have one angle in common. That angle is congruent to itself. This is already one angle of one triangle that is congruent to one angle of the other triangle.

Now notice that each triangle also has an angle that measures 30 degrees. That makes a second angle of one triangle that is congruent to a second angle of the other triangle.
That is enough to prove the triangles are similar.

Now you need to write this as a proper two-column proof with statements on the left side and reasons on the right side.