Congruent Figures & Corresponding Parts (CPCTC)

Reading a congruence statement

In $\triangle ABC \cong \triangle DEF$, match the letters by position: $A \leftrightarrow D$, $B \leftrightarrow E$, and $C \leftrightarrow F$. That correspondence is a promise. It means $\angle A \cong \angle D$, $\angle B \cong \angle E$, and $\angle C \cong \angle F$.

Sides follow the same rule using pairs of letters. $\overline{AB}$ uses the first and second letters, so it corresponds to $\overline{DE}$ — the first and second letters of the other name. Likewise $\overline{BC} \cong \overline{EF}$ and $\overline{AC} \cong \overline{DF}$.

Because the letter order carries all of this information, $\triangle ABC \cong \triangle DEF$ and $\triangle ABC \cong \triangle FED$ are different claims. Never reorder the letters when you copy a congruence statement.

What CPCTC means

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It works in one direction: first establish that the triangles are congruent, then conclude that any pair of corresponding parts is congruent.

This matters in problems and proofs alike. If a question tells you $\triangle CAT \cong \triangle DOG$, you may immediately write $\overline{CA} \cong \overline{DO}$ or $\angle T \cong \angle G$ — no extra work, just careful letter-matching.

Tick marks and arcs

Diagrams mark congruence instead of stating it. Sides with the same number of tick marks are congruent, and angles with the same number of arcs are congruent.

To write a congruence statement from a marked diagram, walk each triangle in an order that visits matching marks at matching moments. If the one-tick side of the first triangle is $\overline{AB}$ and the one-tick side of the second is $\overline{DE}$, then $A$ and $B$ must line up with $D$ and $E$ in the statement. In the diagram below, matching tick marks pair the corresponding sides.

Worked examples

Try one yourself

Common questions