In similar triangles the smallest sides are corresponding, the longest sides are corresponding, and so on.
B
b
Identify corresponding sides and set up proportions containing x and y.
C
c
The pentagons have different positions, rotations. and sizes.
A
a
They are not similar, see solution.
B
b
x=33 and y=10
C
c
Possible Sequence: Translation → Rotation → Dilation
Practice makes perfect
a
If the triangles are similar, the ratio of corresponding sides must be the same. In similar figures the smallest sides must be corresponding, the longest sides must be corresponding, and so on. With this information we can set up the following equation.
3/6 ? = 5/10 ? = 4/7
All of these quotients must be the same for the triangles to be similar. Therefore, by calculating the quotients we can investigate if the triangles are similar.
0.5 = 0.5 ≠0.571428...
The triangles are not similar.
b
This time we know that the pentagons are similar, so we know that the ratio of the corresponding sides will be the same. Therefore, by identifying corresponding sides we can set up two proportions — one containing x and the other containing y.
Examining the diagram, we see that the pentagons have different positions, rotations, and sizes. Therefore, we would need to perform a translation, a rotation, and a dilation to make the pentagon on the left map onto the pentagon on the right. Notice that there are different ways of solving, but this time let's first perform a translation to make two corresponding vertices map onto each other.
Next, we will perform a rotation to make two of the corresponding sides map onto each other.
Finally, we will dilate the big pentagon to make all corresponding sides map onto each other.
