Integrated Math 1 / Unit 8: Transformations and Congruence
8.5 Congruence and Rigid Motions
Notes
Two figures are congruent if a sequence of rigid motions maps one onto the other. Congruent figures have equal corresponding sides and angles.
- The order of letters shows correspondence: $\triangle ABC \cong \triangle DEF$ means $A \leftrightarrow D$, $B \leftrightarrow E$, $C \leftrightarrow F$.
- Corresponding parts of congruent triangles are congruent (CPCTC).
- Example: if $\angle A = 50^\circ$ and $\angle B = 60^\circ$, then $\angle C = 70^\circ$, so $\angle F = 70^\circ$.
- Congruent is not the same as similar: similar figures may differ in size.
Practice
What is true if two figures are congruent?
Congruence means same shape and size, which is exactly when rigid motions can match them.
$\triangle ABC \cong \triangle DEF$, $\angle A = 50^\circ$ and $\angle B = 60^\circ$. What is $\angle F$?
$\angle C = 180^\circ - 50^\circ - 60^\circ = 70^\circ$, and $F$ corresponds to $C$.
$\triangle ABC \cong \triangle XYZ$ with $AB = 7$, $BC = 9$ and $AC = 5$. What is $YZ$?
$YZ$ corresponds to $BC$ because $Y \leftrightarrow B$ and $Z \leftrightarrow C$.
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