Question

Triangle ABC is reflected across the y-axis to form the triangle A′B′C′, then dilated with a factor of 1∕3 to form triangle A″B″C″. Which of the following statements is true for ΔABC and ΔA″B″C″?Question 5 options:A) ΔABC and ΔA″B″C″ are similar triangles.B) ΔABC and ΔA″B″C″ are congruent triangles.C) ΔABC and ΔA″B″C″ are neither similar nor congruent.D) There's not enough information to identify whether ΔABC and ΔA″B″C″ are congruent or similar.

Answer 1

Given that:

- Triangle ABC is reflected across the y-axis to form the triangle A'B'C'.

- It was then dilated by the following scale factor in order to form triangle A"B"C":

$k=\frac{1}{3}$

You need to remember the following definitions in order to solve the exercise:

1. In Transformations, the original figure is called "Pre-Image" and the figure obtained after the transformation is called "Image".

2. When the transformation is a Reflection, the Image and the Pre-Image have the same size and shape.

3. In Dilations, the Image and the Pre-Image have the same shape but their sizes are different.

4. Two figures are similar when their corresponding angles are congruent and the ratios of the lengths of their corresponding sides are proportional.

5. Two figures are congruent when they have the same size and the same shape.

Then, you can conclude that:

• The triangles ABC and A'B'C' have the same shape and size. Therefore, they are congruent.

,

• The triangles ABC and A"B"C" have different sizes, therefore, they are not congruent.

,

• Knowing that the triangles ABC and A'B'C' are congruent, and knowing that A'B'C' has dilated to get the triangle A''B''C'', you can determine that the triangles ABC and A"B"C" are similar.

Hence, the answer is: Option A.