Question

Which descriptions from the list below accurately describe the relationshipbetween AQRS and ATUV? Check all that apply.ongruent

Answer 1

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

`\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) \\ \\ (QR)/(TU)=(QS)/(TV)=(RS)/(UV)=(1)/(3)=1\colon3 \end{gathered}`

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: