Congruent Triangles to the Rescue

Learning Focus

Use triangle congruence and CPCTC to find unknown measures and justify claims.

Big idea

CPCTC means corresponding parts of congruent triangles are congruent. The process:

• Prove triangles congruent with SSS, SAS, ASA, AAS, or HL.
• Conclude that other corresponding parts are equal.
• In an isosceles triangle, base angles are equal.

Worked example

$\triangle ABC\cong\triangle DEF$, $m\angle A=(3x+5)^\circ$, $m\angle D=50^\circ$.

By CPCTC: $3x+5=50\Rightarrow x=15$.

An isosceles triangle with a $40^\circ$ apex has base angles $\frac{180-40}{2}=70^\circ$.

Takeaways

• Prove congruence first.
• Then use CPCTC.
• Set corresponding measures equal and solve.