Question

34

Question 6 Multiple Choice Worth i pones)

(03.02 MC)

The vertices of AABC are A (1,5), B (3,9), and C (5,3). The vertices of ADEF are D (-3, 3), E (-2,5), and F (-1. 2). Which conclusion is true about the triangles?

The ratio of their corresponding sides

,

They are congruent by the definition of congruence in terms of rigid motions.

The ratio of their corresponding angles is 1:3.

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

Answer 1

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

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.