Final Answer:
Using CPCTC (Corresponding Parts of Congruent Triangles are Congruent) after proving that two triangles are congruent, we can conclude that their corresponding angles, sides, and other geometric properties are also congruent.
Step-by-step explanation:
CPCTC is a powerful principle in geometry that extends the congruence of triangles to their corresponding parts. After establishing the congruence of two triangles, three key conclusions can be drawn using CPCTC. Firstly, the corresponding angles of the congruent triangles are equal. This can be denoted as ∠A_1 ≅ ∠A_2, ∠B_1 ≅ ∠B_2, and ∠C_1 ≅ ∠C_2, where ∠A_1, ∠B_1, and ∠C_1 are angles of the first triangle, and ∠A_2, ∠B_2, and ∠C_2 are angles of the second triangle.
Secondly, the corresponding sides of the congruent triangles are of equal length. This can be expressed as AB_1 ≅ AB_2, BC_1 ≅ BC_2, and AC_1 ≅ AC_2, where AB_1, BC_1, and AC_1 are sides of the first triangle, and AB_2, BC_2, and AC_2 are sides of the second triangle.
Lastly, other geometric properties that are dependent on congruent triangles, such as medians, altitudes, and angle bisectors, can also be concluded to be congruent through the application of CPCTC. This comprehensive congruence principle allows for a thorough exploration of the relationships between corresponding parts of congruent triangles, facilitating further analysis and problem-solving in geometry.