Answer:
1. Not similar
2. Similar, ABC is similar to FED by SSS
Step-by-step explanation:
1. Not similar.
The interior angles of a triangle always have to add up to 180, and since the first triangle has angles 30 degrees and 90 degrees, you know the third angle will have to be 180 - 30 - 90 = 60 degrees.
The second triangle's third angle will have to be 50 degrees because 180 - 90 - 40 = 50 degrees.
Since the three angles of the triangle are not the same, they are not similar.
2. Similar, ABC is similar to FED by the SSS triangle similarity postulate.
First, AB is similar to FE because AB = 15 and FE = 5, so the scale factor is 3
Next, BC is similar to ED because BC = 9 and ED = 3, so the scale factor for these sides is also 3
Lastly, CA is similar to DF because CA = 12 and DF = 4, so the scal factor for this is also 3.
Since the scale factor for all of the sides is 3, these two triangles are similar.
