Question

If ABC ≅ DEF, which congruences are true by CPCTC? Check all that apply.

a) A ≅ E
b) C ≅ D
c) E ≅ F

Answer 1

Using CPCTC, Angle A is congruent to Angle E and Angle C is congruent to Angle D. Other corresponding parts of the congruent triangles will also be congruent.

Step-by-step explanation:

When triangles ABC and DEF are congruent (ABC ≅ DEF), CPCTC (Corresponding Parts of Congruent Triangles are Congruent) applies, which means that all corresponding sides and angles are congruent. Specifically:

• Angle A is congruent to Angle E (A ≅ E).
• Angle B is congruent to Angle F (B ≅ F).
• Angle C is congruent to Angle D (C ≅ D).
• Side AB is congruent to Side DE (AB ≅ DE).
• Side BC is congruent to Side EF (BC ≅ EF).
• Side CA is congruent to Side FD (CA ≅ FD).

Therefore, the correct congruences by CPCTC are:

1. A ≅ E
2. C ≅ D
3. E ≅ F (this is also true, but since it wasn't listed as an option in the question stem, you may have accidentally included it. Within the specified choices, this would not be applicable).