Question

Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.

Answer 1

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

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