Question

Triangle ABC has Vertices A(1, 2), B(3, 5), and C(4, 3). Using the origin as the center of dilation, Triangle ABC is dilated by a scale factor of 3 to create Triangle A ′ B ′ C ′ . Which statement can be used to justify that Triangle ABC is similar to Triangle A ′ B ′ C ′ ?

Answer 1

Answer:

AA ≅ AA postulate

Step-by-step explanation:

Given

$A=(1,2)$

$B = (3,5)$

$C = (4,3)$

$k = 3$ --- scale factor

Required

Determine which statement that justifies the similarities between ABC and A'B'C'

When ABC is dilated by a scale factor of 3 to form A'B'C', the sides A'B'C are 3 times as large as the sides of ABC.

However, all three angles of both triangles remain the same. This is so, because dilation do not affect angles.

So, a statement that can be used to justify the similarities is:  AA ≅ AA