Unit 2, Lesson 6
Similarity
Grade 8
6.1
Warm-up
Which 3 go together? Why do they go together?
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Which 3 go together? Why do they go together?
Triangle and triangle are similar. Find a sequence of translations, rotations, reflections, and dilations that shows this.
Hexagon and hexagon are similar. Find a sequence of translations, rotations, reflections, and dilations that shows this.
Sketch figures similar to Figure A that use only the transformations listed to show similarity.
Your teacher will give you and your partner a set of cards. Each set contains five cards for Partner A and a different set of five cards for Partner B.
Using only the cards in your set, find one or more ways to show that triangle and triangle are similar.
Compare your method with your partner’s method. How are your methods similar? How are they different?
Let’s show that triangle is similar to triangle :
Two figures are similar if one figure can be transformed into the other by a sequence of translations, rotations, reflections, and dilations. There are many correct sequences of transformations, but we only need to describe one to show that two figures are similar.
One way to get from triangle to triangle follows these steps:
Another way to show that triangle is similar to triangle would be to dilate triangle by a scale factor of with center of dilation at , then translate to , then rotate it clockwise around , and finally reflect it across the vertical line containing so it matches up with triangle .
Two figures are similar if one can fit exactly over the other after transformations.
This figure shows triangle is similar to triangle .
A sequence of transformations. Triangle ABC is rotated around point B and and then dilated with center point O to fit exactly over Triangle DEF. Triangle ABC is similar to triangle DEF.