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

Correct choices:
- RST is congruent to R’’S’’T’’
- Angle R is congruent to angle R′ is congruent to angle R′′
- TS is congruent to T′S′ is congruent to T′′S′′

Reason: reflections and translations are rigid motions, so they preserve distances and angle measures, and congruence is transitive (so RST ≅ R′S′T′ and R′S′T′ ≅ R′′S′′T′′ imply RST ≅ R′′S′′T′′). That also gives corresponding angles and corresponding side lengths are congruent.

The other two statements are false: RS, ST, TR are not all equal (RS = √5, ST = √2, TR = 3), so the triangle is neither equilateral nor equiangular.