Geometry / Unit 5: Congruent Triangles
5.5 Using CPCTC
Notes
CPCTC means "Corresponding Parts of Congruent Triangles are Congruent."
- First prove the triangles congruent (SSS, SAS, ASA, AAS or HL).
- Then use CPCTC to conclude that other matching sides or angles are congruent.
- Example: $\overline{AB} \cong \overline{CB}$ and $\overrightarrow{BD}$ bisects $\angle ABC$, with $D$ on $\overline{AC}$. Then $\triangle ABD \cong \triangle CBD$ by SAS (with $\overline{BD} \cong \overline{BD}$), so $\overline{AD} \cong \overline{CD}$ by CPCTC.
Practice
$\triangle ABC \cong \triangle DEF$ by SAS. Which conclusion follows from CPCTC?
Corresponding parts follow the letter order: $C \leftrightarrow F$.
In a proof, when should CPCTC be used?
CPCTC needs triangles that are already known to be congruent.
$\triangle PQR \cong \triangle PSR$, $m\angle Q = 3x + 4$ and $m\angle S = 5x - 12$. Find $m\angle Q$.
By CPCTC, $3x + 4 = 5x - 12$, so $x = 8$ and $m\angle Q = 28^\circ$.
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