Proving Figures Are Similar Using Transformations

Is Rectangle Q similar to Rectangle R?

Why or Why not?

• Yes! The corresponding angles and congruent.

• No! They have different areas.

• No! The corresponding angles are congruent but the corresponding sides aren't proportional.

• Yes! They are both rectangles that are different sizes

In a proof of similar figures you must prove 2 things:

• A series of rigid motions puts one shape on top of the other proving Corresponding Angles are Congruent

• Corresponding Sides are Congruent

• A series of rigid motions only.

• Corresponding Angles are Proportional

• A dilation places one shape on top of the other proving the corresponding angles are congruent.

Which step is incorrect?

• Step 2

• Step 3

• Step 4

• Step 5

• Step 6

Answer explanation

Which statement provides a valid justification for why all circles are similar?

• A

• B

• C

• D

What transformations can you use to show Triangle ABC and Triangle DEF are similar?

• Rotation 180° CW, Dilation by 2

  Translation

• Rotation 90° CW, Dilation by 2

  Translation

• Rotation 90° CW, Dilation by 1/2, Translation

• Rotation 180° CW, Dilation by 1/2

  Translation

A dilation with center (0,0) and a scale factor of 1/2 maps ABC to ADE.

• Yes. A dilation with center (0,0) and a scale factor of 1/2 maps ABC to ADE.

• Yes. A dilation with center (0,0) and a scale factor of 2 maps ABC to ADE.

• Yes. A translation 2 units up and 4 units right maps ADE to ABC.

• No. ABC is not similar to ADE.

Yes. A dilation with center (0,0) and a scale factor of 1/2 maps ABC to ADE.

• Yes. A dilation with center (0,0) and a scale factor of 1/2 maps ABC to ADE.

• Yes. A dilation with center (0,0) and a scale factor of 2 maps ABC to ADE.

• Yes. A translation 2 units up and 4 units right maps ADE to ABC.

• No. ABC is not similar to ADE.

Which of the following describes the sequence of transformations shown?

• Reflect across the x-axis and then rotate -90 degrees around the origin

• Rotate -90 degrees around the origin and then translate down.

• Reflect across the x-axis and then reflect across the y-axis.

• Translate up and then rotate 90 degrees about the origin.

Triangle ABC is congruent to triangle DEF. Which series of transformations maps DEF onto ABC?

• dilation followed by a reflection

• rotation followed by a dilation

• translation followed by a dilation

• rotation followed by a translation

Select all sequences of transformations that show ABC and AED are similar:

• Dilate triangle AED using center A by a scale factor of 2 then reflect over AC

• Reflect triangle AED over line AC, then dilate using center A by a scale factor of 2

• Translate triangle AED by directed line segment DC , then dilate using center C by scale factor 2.