Question

If AJKL ≅ ARST, which congruences are true by CPCTC? Check all that apply.

A) ∠AJK ≅ ∠ARS
B) ∠JKA ≅ ∠RST
C) ∠KJA ≅ ∠SRT
D) ∠JAK ≅ ∠RTS

Answer 1

By CPCTC, corresponding parts of congruent triangles are congruent. Therefore, the true congruences for ∠AJK ≅ ∠ARS, ∠JKA ≅ ∠RST, and ∠KJA ≅ ∠SRT are options A, B, and C. Option D cannot be confirmed without additional information.

Step-by-step explanation:

If AJKL ≅ ARST, we can determine which angle congruences are true by using the principle of Corresponding Parts of Congruent Triangles are Congruent (CPCTC). By CPCTC, corresponding angles and sides of congruent triangles are equal in measure. Given this information, we analyze the options provided to identify the true congruences.

• A) ∠AJK ≅ ∠ARS (Correct): Since these are corresponding angles of the congruent triangles.
• B) ∠JKA ≅ ∠RST (Correct): These are also corresponding angles in the congruent triangles.
• C) ∠KJA ≅ ∠SRT (Correct): These angles are corresponding as well and thus are congruent.
• D) ∠JAK ≅ ∠RTS: This option is not necessarily correct because we have no information on whether these triangles are part of a larger figure and this angle correspondence is valid. In a simple case where AJKL and ARST are separate triangles, ∠JAK and ∠RTS are not corresponding angles and thus we cannot conclude they are congruent simply based on the information given.

So, the correct congruences by CPCTC are options A, B, and C.