Can anyone explain clearly what exactly CPCTC(corresponding parts of congruent triangles are congruent)?

Answer 1

For congruent triangles the corresponding angles will always be equal, although the sides may not.

But having said that I want you to understand that the sides will always be proportional.

For example, two triangles are congruent.

If triangle XYZ has sides of 3, 4, and 5, the other congruent triangle ABC will have sides of 15, 20, and 25.

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Answer 2

Congruent.

Answer 3

It means that individual pieces of the two triangles are also congruent.

For example, suppose it is given that triangle ABC is congruent to triangle DEF. If angle A corresponds to angle D, then, by CPCTC, angle A is congruent to angle D (even if angles A and D were not involved in proving the triangles congruent).

Or, suppose that we know that triangle PQR, angle Q, side QR, and angle R are congruent to angle T, side TU, and angle U of triangle STU, respectively. By ASA, the two triangles are congruent. And by CPCTC, you know that angle P is congruent to angle S, side PQ is congruent to side ST, etc.

"Congruent" means the two shapes are identical -- same angles, same length sides. (One of the respondents below is referring to "similar" triangles, which is not the same concept.)

Answer 4

positive rational number that is the area of a right-triangle with three rational number sides.