Answer:
b.
Explanation:
The polygons are similar by the SAS postulate. This means that when you have two triangles that you only know two sides and the angle between those sides, you know if they are similar.
The triangles have the same angle (32°). (Check off one angle).
To check if the sides are similar, find the ratio between the sides in each triangle. If the ratios are the same, it means triangle UVW increased proportionately.
In each triangle, do top side ÷ bottom side.
RST: 10/15 = 0.6777....
UVW: 12/18 = 0.6777.... They have the same ratio.
Side SR is similar to side VU. Side WU is similar to side TR.
Therefore the triangles are similar.
If the smaller triangle has to be labeled ΔRST, then the bigger triangle has to have the angle letters in the same order. You can tell the triangles are rotated the same way, so
∠R ~ ∠S
∠W ~ ∠T
Write the bigger triangle as ΔUVW.
The scale factor means how much the original triangle grew or shrink to become a new similar triangle. Since this is a multiply choice question, we already know the answer is b when we found the order of letters to write the bigger triangle.
If you wanted to find the scale factor, you divide one side in the first triangle by the corresponding side in the second triangle.
For example:
Side SR is similar to side VU.
SR = 10 and VU = 12
Divide SR by VU
SR / VU
= 10/12 Reduce the fraction
= 5/6 Scale factor.