SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define the terms
Similar triangles: Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles
Congruent triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure
Same size: The triangles have same size if they have the same measures for the sides and angles.
Same shape: Similar triangles have the same shape.
STEP 2: Explain the given triangles
It can be seen from the image above that:
The two triangles have same measures for the three angles
The two triangles have equivalent sides which have the ratio 1:3 as seen below
[tex]\begin{gathered} QR=24,TU=72\Rightarrow TU=3(QR) \\ QS=36,TV=108\Rightarrow TV=3(QS) \\ RS=30,UV=90\Rightarrow UV=3(RS) \\ \\ \frac{QR}{TU}=\frac{QS}{TV}=\frac{RS}{UV}=\frac{1}{3}=1\colon3 \end{gathered}[/tex]
STEP 3: Make a conclusion
Since the two triangles have same ratio of corresponding sides and equal pair of corresponding angles, therefore they are similar. Even though they have 3 corresponding angle, they do not have 3 corresponding sides which means that they are not congruent. They do not have same size since Triangle TUV is 3 time bigger than Triangle QRS. Since they are similar, they have same shape.
Hence, the correct options are:
