a The first thing we notice is that corresponding sides have equal lengths. Therefore these are congruent triangles, which means we do not have to perform any dilations. To map one of them onto the other, we first have to perform a translation so that two corresponding vertices map onto each other.
Next, we will rotate one of the triangles so that the longest sides lines up.
Finally, we will mirror one of the triangles in the longest side, which will make them map onto each other.
Let's write the sequence of transformations that shows the figures are similar. Remember that this is just one possible sequence, and the answers can vary.
Translation → Rotation → Reflection
b Again, we notice that corresponding sides have the same lengths. Also, since the figures are apart, we have to perform a translation in order to map one vertex onto its corresponding vertex.
Finally, to make them map onto each other we will rotate one of them.
Let's write the sequence of transformations that shows the figures are similar.
Translation → Rotation
c Since the figures are apart, we first have to perform a translation. Let's translate the smaller circle so that its radius lies on top of the larger circle's radius.
Next, we will rotate the smaller circle so that the radii line up.
Finally, we can dilate the smaller circle to map it onto the larger circle. Since the larger circle has a radius of 10 and the smaller has a radius of 5, we have to dilate the smaller circle with a factor of 105=2 to make them map onto each other.
Let's write the sequence of transformations that shows the figures are similar.
Translation → Rotation→ Dilation
d Just as in Parts A-C the figures are apart, which means we first have to perform a translation to make one of the vertices line up. Let's translate the smaller triangle in this way.
By reflecting the smaller triangle in the horizontal side, we can give them the same rotation.
Finally, we can dilate the smaller triangle to map it onto the larger triangle. Since one of the sides in the larger triangle is 6 and its corresponding side in the smaller triangle is 3, we have to dilate the smaller triangle by a factor of 63=2 to make them map onto each other.
Let's write the sequence of transformations that shows the figures are similar.
Translation → Reflection→ Dilation
