Question

34

Answer 1

Answer:

They are similar by the definition of similarity in terms of a dilation

Step-by-step explanation:

The given vertices of triangle ΔABC are;

A(1, 5), B(3, 9), and C(5, 3)

The vertices of triangle ΔDEF are;

D(-3, 3), E(-2, 5), and F(-1, 2)

Therefore, we get;

The length of segment, $\overline{AB}$ = √((9 - 5)² + (3 - 1)²) = 2·√5

The length of segment, $\overline{BC}$ = √((9 - 3)² + (3 - 5)²) = 2·√10

The length of segment, $\overline{AC}$ = √((5 - 3)² + (1 - 5)²) = 2·√5

The length of segment, $\overline{DE}$ = √((5 - 3)² + (-2 - (-3))²) = √5

The length of segment, $\overline{EF}$ = √((2 - 5)² + (-1 - (-2))²) = √10

The length of segment, $\overline{DF}$ = √((2 - 3)² + (-1 - (-3))²) = √5

∴ $\overline{AB}$/$\overline{DE}$ = 2·√5/(√5) = 2

$\overline{BC}$/$\overline{EF}$ = 2·√10/(√10) = 2

$\overline{AC}$/$\overline{DF}$ = 2·√5/(√5) = 2

The ratio of their corresponding sides are equal and therefore;

ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.