Question

Is there a similarity transformation that maps Triangle ABC to Triangle DEF? If so, identify the similarity transformation and write a similarity statement. Explain your answer.

Answer 1

Answer:

Yes, there is a similarity transformation that maps triangle ABC to Triangle DEF.

Step-by-step explanation:

Similarity transformation;

Triangle DEF has been transformed(dilated) by a factor of 2.

Since each dimension is twice that of the triangle ABC.

Two triangles are similar if their corresponding sides are congruent and corresponding angles are congruent.

Similarity statement:

ΔABC $\sim$ ΔDEF

these two triangles are similar because;

$\frac{AB}{DE}= \frac{4}{8} = \frac{1}{2}$

$\frac{AC}{DF}= \frac{4}{8} = \frac{1}{2}$

$\frac{BC}{EF}= \frac{3}{6} = \frac{1}{2}$

⇒ $\frac{AB}{DE}=\frac{AC}{DF} =\frac{BC}{EF}$