Question

Entrance Ticket: Sequencing with Dilations у 5 Describe the two sequences of ansformations that can be used to emonstrate similarity between triangles BC and DEC. D 2. Identify the algebraic rule (general rule) of each transformation. OC -5 E 3. Explain the relationship between triangles ABC and DEC (congruent or similarity). Explain how you know. un

Answer 1

1. To get the traingle DEC from the triangle ABC you use the next transformations:

A reflection over the y-axis

A dilatation

2. Reflection: The points in the traingle ABC become in points A'B'C following the next rule

`ABC(x,y)\rightarrow A^(\prime)B^(\prime)C^(\prime)(-x,y)`

Dilatation: The traingle A'B'C is dilated to get DECfollowing the next rule:

(As you can see the triangle ABC is half size of the triangle DEC, then the scale factor is: 2:1)

`A^(\prime)B^(\prime)C(x,y)\rightarrow DEC(2x,2y)`

3. The triangles ABC and DEC are similar, as their corresponding sides are proportional but not the same.

(congruent triangles have the same measure in their corresponding sides)