Question

Figure RST on the graph is reflected over the y-axis creating figure R’S’T’. Figure R’S’T’ is translated down 2 units and left 1 unit creating R’’S’’T’’. On a coordinate plane, triangle R S T has points (1, 1), (2, 3), (1, 4). Triangle R prime S prime T prime has points (negative 1, 1), (negative 2, 3), (negative 1, 4). Triangle R double-prime S double-prime T double-prime has points (negative 2, negative 1), (negative 3, 1), (negative 2, 2). Tyler knows that RST Is congruent to R’S’T’ because reflections produce congruent figures. He also knows that R’S’T’ Is congruent to R’’S’’T’’ because translations produce congruent figures. What can Tyler determine based on these two statements? Check all that apply. RST Is congruent to R’’S’’T’’ RS Is congruent to ST Is congruent to TR Angle R is congruent to angle S is congruent to angle T Angle R is congruent to angle R prime is congruent to angle R double-prime TS Is congruent to T’S’ Is congruent to T’’S’’

Answer 1

a d e

Explanation:

Answer 2

RST Is congruent to R’’S’’T’’

Angle R is congruent to angle R prime is congruent to angle R double-prime

TS Is congruent to T’S’ Is congruent to T’’S’’

Explanation:

we know that

A reflection and a translation are rigid transformation that produce congruent figures

If two or more figures are congruent, then its corresponding sides and its corresponding angles are congruent

In this problem

Triangles RST, R'S'T and R''S''T'' are congruent

That means

Corresponding sides

RS≅R'S'≅R''S''

ST≅S'T'≅S''T''

RT≅R'T'≅R''T''

Corresponding angles

∠R≅∠R'≅∠R''

∠S≅∠S'≅∠S''

∠T≅∠T'≅∠T''

therefore

RST Is congruent to R’’S’’T’’

Angle R is congruent to angle R prime is congruent to angle R double-prime

TS Is congruent to T’S’ Is congruent to T’’S’’