Question

determine the following. *

1. δrst is reflected to form δrst. select all of the statements that are true by cpctc.

a (overline{rt} cong overline{rt})
b (overline{sr} cong overline{st})
c (δrst cong δrst)
d (∠t cong ∠r)
e (∠r cong ∠r)
a
b
c
d
e
this is a required question

Explanation:

1. CPCTC Definition: CPCTC (Corresponding Parts of Congruent Triangles are Congruent) applies after proving triangles congruent. A reflection preserves congruence, so $\triangle RST \cong \triangle R'S'T'$ (by reflection, a rigid transformation).
2. Analyzing Option A: $\overline{RT}$ and $\overline{R'T'}$ are corresponding sides of $\triangle RST$ and $\triangle R'S'T'$. By CPCTC, corresponding sides are congruent, so $\overline{RT} \cong \overline{R'T'}$ is true.
3. Analyzing Option B: $\overline{S'R'}$ corresponds to $\overline{SR}$, not $\overline{ST}$. Thus, $\overline{S'R'} \cong \overline{ST}$ is false.
4. Analyzing Option C: $\triangle RST \cong \triangle R'S'T'$ is true by reflection (rigid transformation), but this is the congruence of the triangles themselves, not a "part" of the triangle. CPCTC refers to parts (sides/angles) of congruent triangles, so this is not a CPCTC statement (it is the congruence used to apply CPCTC).
5. Analyzing Option D: $\angle T$ corresponds to $\angle T'$, not $\angle R'$. Thus, $\angle T \cong \angle R'$ is false.
6. Analyzing Option E: $\angle R$ and $\angle R'$ are corresponding angles of $\triangle RST$ and $\triangle R'S'T'$. By CPCTC, corresponding angles are congruent, so $\angle R \cong \angle R'$ is true.

Answer:

A. $\overline{RT} \cong \overline{R'T'}$, E. $\angle R \cong \angle R'$