Proving Similarity I—Using Transformations
Similarity: Two objects are similar if one of the objects can be carried exactly onto the other using only a
sequence of dilations, reflections, rotations, and/or translations.
Determine if the following figures are similar using the definition of similarity above. If they are similar,
specify in detail the sequence of transformations required. If they are not similar, give specific evidence
that justifies your conclusion.
10
1.
8
6
4
2
20
15
10
5
5
10
15
20
5
10
15
20
2
4
6
8
10
2.
10
8
6
4
2
20
15
10
5
2
4
6
8
10
10
3.
8
6
4
2
20
15
10
5
5
10
15
20
5
10
15
20
2
4
6
8
10
4.
10
8
6
4
2
20
15
10
5
2
4
6
8
10
5.
6. After exploring dilations and similarity for a while, Alicia came up with Alicia’s Conjecture:
All circles are similar to one another. Investigate Alicia’s Conjecture to see if you can
conclusively prove or disprove it. (Hint: construct two circles of different sizes and if you can
always find a sequence of transformations of one onto the other.)
7. After working on Alicia’s Conjecture for a while, Beto’s mind wandered in an interesting
direction. He proclaimed Beto’s Conjecture: All parabolas are similar to one another.
Investigate Beto’s Conjecture to see if you can conclusively prove or disprove it.