Question

triangle abc is reflected across the line y = 2x to form triangle rst. select all of the true statements.
ab ≅ rs
ab ≅ 2 · rs
△abc ≅ △rst
m∠bac ≅ m∠str
m∠bac ≅ 2 · m∠str

Explanation:

Step1: Recall the properties of reflection

When a figure is reflected, the reflected figure is congruent to the original figure. So, \(\triangle ABC\cong\triangle RST\).

Step2: Analyze side - length relationships in congruent triangles

In congruent triangles, corresponding sides are congruent. Since \(\triangle ABC\cong\triangle RST\), \(AB\) corresponds to \(RS\), so \(AB\cong RS\).

Step3: Analyze angle - measure relationships in congruent triangles

In congruent triangles, corresponding angles are congruent. So, \(m\angle BAC=m\angle STR\) (because \(\angle BAC\) in \(\triangle ABC\) corresponds to \(\angle STR\) in \(\triangle RST\) as \(\triangle ABC\cong\triangle RST\)).

Answer:

\(\triangle ABC\cong\triangle RST\), \(AB\cong RS\)