Question

Determine whether each pair of figures is similar. Justify your answer. DEF is not similar to BAC . Corresponding angles are not the same. DEF-BAC because the corresponding angles of each triangle are congruent. The ratio of the corresponding sides is 1/2 . DEF-ABC because the corresponding angles of each triangle are congruent. The ratio of the corresponding sides is 2. DEF is not similar to BAC . The ratios of the corresponding sides are not the same.

Answer 1

Answer:

Option (2)

Step-by-step explanation:

Two triangle are similar when,

1). Two or more than two angles of the given triangles are equal in measure.

2). Ratio of the corresponding sides are same.

In the triangles ΔDEF and ΔBAC,

m(∠A) = m(∠E) = 58°

m(∠B) = m(∠D) = 53°

m(∠C) = m(∠F) = 69°

And ratio of the corresponding sides,

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

$\frac{2.6}{5.2}=\frac{2.8}{5.6}=\frac{3.1}{6.2}$

$\frac{1}{2}=\frac{1}{2}=\frac{1}{2}$

Therefore, ΔDEF ~ ΔBAC

Option (2) will be the answer.