Dilation and Parallel Triangles

Figures are similar if there is a sequence of _____ motions AND

a ________ that fits one on top of the other.

• non-rigid, dilation

• rigid, dilation

• translation, dilation

• dilations, rigid

Similar figures have ​ (a)   corresponding sides and ​ (b)   corresponding angles.

• proportional

• congruent

Are these triangles similar?

• Yes, by SAS Similarity

• Yes, by AA Similarity

• No

• Not enough information

Is line BC parallel to line MN? Choose the best justification.

• Line BC is parallel to line MN because triangle ABC is a dilation of triangle AMN by a scale factor of 4 from point A.

• Line BC is parallel to line MN because triangle ABC is a dilation of triangle AMN by a scale factor of 3 from point A.

• Line BC is parallel to line MN because triangle ABC is a dilation of triangle AMN by a scale factor of 4/3 from point A.

• Line BC is not parallel to line MN because there is no dilation that sends triangle ABC to triangle AMN.

Triangle WXY can be taken to triangle W’X’Y’ using rigid motions and dilations. Select all the equations that are true.

Triangle ABC is similar to triangle WXY. What scale factor is required to dilate triangle ABC so that its image, A'B'C', is congruent to triangle WXY?

• 3

What do the properties of dilations tell you about angle A'?

Triangles 𝐴𝐵𝐶 and 𝐷𝐸𝐹 are similar. Determine the exact lengths of segments 𝐷𝐹 and 𝐸𝐹.

a

b

2.01

2.68

Triangle 𝐸𝐹𝐺 is a dilation of triangle 𝐴𝐵𝐶 with center 𝐵 and a scale factor of 3. Which of the following illustrates triangle 𝐸𝐹𝐺 with respect to triangle 𝐴𝐵𝐶?

• 
• 
• 
• 

Triangles EFC, and CBA are similar. Which sequence of transformation will carry from Triangle

• A translation, then a dilation.

• A dilation, followed by another dilation.

• A reflection, then dilation

• A rotation, then a dilation