Question

1. 2. In a well-written paragraph or paragraphs describe how dilations create similar triangles and explain ways to prove two triangles are similar. Set a timer for 40 minutes. If you dedicate 40 minutes to completing this writing assignment with no distractions, I believe you will have complete and thorough answers to the questions in your assignment. Peer Feedback: Over the weekend, you will choose one person to respond to (only one response per personl) using the clarify or elaborate discussion cards 3.

Answer 1

we know that

A non rigid transformations produce similar figures

Example of non rigid transformation is a dilation

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

Example

You have the triangle ABC

Apply dilation with a scale factor equal 2 to triangle ABC to produce triangle A'B'C'

so

Triangle ABC and triangle A'B'C' are similar

because

AB/A'B'=BC/B'C'=AC/A'C'

The image of the dilation (triangle A'B'C') is an elangerment of triangle ABC (because the scale factor is greater than 1)

the ratio of the corresponding sides is equal to the scale factor

so

AB/A'B'=BC/B'C'=AC/A'C'=1/2

or

A'B'/AB=B'C'/BC=A'C'/AC=2

Example with length sides

we have

AB=3 units

BC=4 units

AC=5 units

scale factor=2

therefore

A'B'=3(2)=6 units

B'C'=4(2)=8 units

A'C'=5(2)=10 units

If the triangles are similar

then the ratio of its corresponding sides is proportional

so

A'B'/AB=B'C'/BC=A'C'/AC=2

substitute

6/3=8/4=10/5=2

2=2=2=2------ > is true

that means

the triangles are similar

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