koissei
contestada

Triangle \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime is the result of dilating \triangle ABC△ABCtriangle, A, B, C about point AAA by a scale factor of \dfrac23
3
2
​
start fraction, 2, divided by, 3, end fraction.

Determine whether each claim about the properties of \triangle ABC△ABCtriangle, A, B, C and \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime is true or false.

Triangle triangle ABCA B C triangle A prime B prime C prime is the result of dilating triangle ABCABCtriangle A B C about point AAA by a scale factor of dfrac23 class=
Relax

Respuesta :

The shape of the image of ΔABC following a dilation by a scale factor of [tex]\dfrac{2}{3}[/tex] is the same as the shape of ΔABC but the sizes of the sides of ΔA'B'C' are [tex]\dfrac{2}{3}[/tex] smaller

The correct options with regards the given statements are;

  • The measure of ∠B and ∠B' are equal is True
  • The coordinates of A and A' are the same is True

Reasons:

The dilation lengths of the sides of ΔABC are AB, AC, BC

The given scale factor of dilation = [tex]\dfrac{2}{3}[/tex]

Therefore;

The lengths of the sides of ΔA'B'C' are [tex]\dfrac{2}{3} \cdot \overline {A'B'}[/tex], [tex]\dfrac{2}{3} \cdot \overline {A'C'}[/tex], [tex]\dfrac{2}{3} \cdot \overline {B'C'}[/tex]

Which gives;

[tex]\dfrac{\overline{A'B'}}{\overline{AB}}} = \dfrac{\overline{A'C'}}{\overline{AC}}} = \dfrac{\overline{B'C'}}{\overline{BC}}} = \dfrac{2}{3}[/tex]

Given that the ratio of the corresponding sides of ΔABC and ΔA'B'C' are equal, ΔABC is similar to ΔA'B'C' by triangle similarity theorem

Therefore;

∠A = ∠A', ∠B = ∠B', and ∠C = ∠C' by definition of triangle similarity

Which gives;

The statement; The measure of ∠B and ∠B' are equal is True

Second part;

The center of dilation of ΔABC is point A, therefore, the distance between point A and point A' following a dilation is zero

Therefore, given that there is no difference, we have;

The coordinates of point A = The coordinates of point A'

Therefore;

The statement, the coordinates of A and A' are the same is True

Learn more here:

https://brainly.com/question/2584916

Ver imagen oeerivona

Otras preguntas