Which triangle similarity statement is correct?
Find the corresponding angles.
Angle GRS and angle TRA are vertical angles, so they are congruent.
Angle SGR and angle TAR are corresponding angles, but they are not necessarily congruent.
Angle RGS and angle RAT are corresponding angles, but they are not necessarily congruent.
Angle GSR and angle RTA are corresponding angles, but they are not necessarily congruent.
Check if the sides are proportional.
GR/TR = 36/18 = 2
RS/RA = 45/15 = 3
The sides are not proportional.
GR/RA = 36/15 = 12/5
RS/TR = 45/18 = 5/2
The sides are not proportional.
Check the similarity of $\triangle$ GRS and $\triangle$ ART.
$\frac{GR}{AR} = \frac{36}{15} = \frac{12}{5}$
$\frac{RS}{RT} = \frac{45}{18} = \frac{5}{2}$
The ratios of corresponding sides are not equal, so the triangles are not similar.
Check the similarity of $\triangle$ GRS and $\triangle$ TRA.
$\frac{GR}{TR} = \frac{36}{18} = 2$
$\frac{RS}{RA} = \frac{45}{15} = 3$
The ratios of corresponding sides are not equal, so the triangles are not similar.
Check the similarity of $\triangle$ GRS and $\triangle$ RTA.
Angle GRS and angle RTA are not congruent.
$\frac{GR}{RT} = \frac{36}{18} = 2$
$\frac{RS}{RA} = \frac{45}{15} = 3$
The ratios of corresponding sides are not equal, so the triangles are not similar.
Consider triangle GRS and triangle TRA.
Angle S is congruent to angle A.
GR/TR = 36/18 = 2
RS/AR = 45/15 = 3
Since the ratio of corresponding sides is not equal and there's only one pair of congruent angles, triangles GRS and TRA are not similar.
Consider triangle GRS and triangle TAR.
$\angle$GRS $\cong$ $\angle$TRA (Vertical angles)
GR/AR = 36/15 = 12/5 = 2.4
RS/TR = 45/18 = 5/2 = 2.5
Since the ratio of corresponding sides including the vertical angles is not equal, then triangle GRS is not similar to triangle TAR. Hence B is not the correct answer.
$\boxed{\text{None of the options are correct.}}$
None of the options are correct.
Answered
