Triangle pqr is transformed to triangle p'q'r'. triangle pqr has vertices p(3, −6), q(0, 9), and r(−3, 0). triangle p'q'r' has vertices p'(1, −2), q'(0, 3), and r'(−1, 0). plot triangles pqr and p'q'r' on your own coordinate grid. part a: what is the scale factor of the dilation that transforms triangle pqr to triangle p'q'r'? explain your answer. (4 points) part b: write the coordinates of triangle p"q"r" obtained after p'q'r' is reflected about the y-axis. (4 points) part c: are the two triangles pqr and p''q''r'' congruent? explain your answer. (2 points

(A)
The transformation from PQR to P'Q'R' is a dilation, with the scale factor equal to P'Q'/PQ=Q'R'/QR=R'P'/RP=1/3
Scale factor is the ratio of the image (dilated) linear dimension divided by the preimage (original) linear dimension.

(B)
When reflected about the y-axis, the sign of the x-coordinates are reversed.  All other values remain unchanged, i.e. (x,y)->(-x,y)
Therefore
P'(1, −2)  -> P"(-1,-2)
Q'(0, 3) -> Q"(0,3)
R'(−1, 0) -> R"(1,0)

(C)
PQR and P"Q"R" are not congruent, since P"Q"R" has undergone two transformations. 
The first transformation is a dilation with a scale factor of 1/3, which does not preserve dimensions, but preserves angles.  
The second transformation is a reflection, which preserves both dimensions and angles.
Therefore, P'Q'R' is congruent to P"Q"R".
PQR is NOT congruent to P"Q"R", but is similar to it (preservation of angles).

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle