Adri3039592
contestada

Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.
AB = RS
AB = 2RS
ABC ~ RST
ABC = RST
m<BAC = m<SRT
m<BAC = 2m<SRT​

Respuesta :

The reflection transformation in the question is a rigid transformation,

therefore, the image and the preimage are congruent.

The statements that are true are;

  • AB = RS
  • ∠ABC ~ ∠RST
  • ΔABC = ΔRST
  • m∠BAC = m∠SRT

Reasons:

The given parameter are;

Triangle ΔABC is reflected across the line 2·X, to map onto triangle ΔRST

Required:

To select the true statements

Solution:

A reflection is a rigid transformation, therefore, the distance between corresponding points on the image and the preimage are equal.

Therefore;

AB = RS

BC = ST

AC = RT

Given that the image formed by a reflection is congruent to the preimage, we have;

ΔABC ≅ ΔRST

∠ABC ≅ ∠RST

m∠ABC = m∠RST by the definition of congruency

∠BCA ≅ ∠STR

m∠BCA = m∠STR by the definition of congruency

∠BAC ≅ ∠SRT

m∠BAC = m∠SRT by the definition of congruency

Therefore, the true statements are;

  • AB = RS; Image formed by rigid transformation
  • ∠ABC ~ ∠RST; Definition of similarity
  • ΔABC = ΔRST; By definition of congruency
  • m∠BAC = m∠SRT; by the definition of congruency

Learn more here:

https://brainly.com/question/11787764

Otras preguntas