Question

figure rst on the graph is reflected over the y - axis creating figure rst. figure rst is translated down 2 units and left 1 unit creating rst. tyler knows that ( rstcong rst ) because reflections produce congruent figures. he also knows that ( rstcong rst ) because translations produce congruent figures. what can tyler determine based on these two statements? choose three correct answers. ( rscong stcong tr ) ( rstcong rst ) ( angle rcongangle scongangle t ) ( tscong tscong ts ) ( angle rcongangle rcongangle r )

Explanation:

Step1: Understand congruence properties

Congruence is transitive. If \(A\cong B\) and \(B\cong C\), then \(A\cong C\). Also, congruent figures have corresponding parts congruent.

Step2: Analyze \(RST\cong R'S'T'\) and \(R'S'T'\cong R''S''T''\)

By transitive property of congruence, \(RST\cong R''S''T''\).

Step3: Analyze corresponding parts

Since \(RST\cong R'S'T'\) and \(R'S'T'\cong R''S''T''\), for corresponding sides \(TS\), \(T'S'\), \(T''S''\) (because reflections and translations preserve side - lengths) and for corresponding angles \(\angle R\), \(\angle R'\), \(\angle R''\) (because reflections and translations preserve angle - measures).

Answer:

\(RST\cong R''S''T''\), \(TS\cong T'S'\cong T''S''\), \(\angle R\cong\angle R'\cong\angle R''\)