Geometry / Unit 5: Congruent Triangles
5.2 Congruent Figures
Notes
Congruent figures have the same size and shape. All matching (corresponding) sides and angles are congruent.
- In a congruence statement, the order of letters shows which parts match: $\triangle ABC \cong \triangle DEF$ means $A \leftrightarrow D$, $B \leftrightarrow E$, $C \leftrightarrow F$.
- So $\overline{AB} \cong \overline{DE}$, $\overline{BC} \cong \overline{EF}$, $\angle C \cong \angle F$, and so on.
- Third Angles Theorem: if two angles of one triangle are congruent to two angles of another, the third angles are congruent.
Practice
$\triangle JKL \cong \triangle MNP$. Which side is congruent to $\overline{KL}$?
$K \leftrightarrow N$ and $L \leftrightarrow P$.
$\triangle ABC \cong \triangle XYZ$, $m\angle A = 40^\circ$ and $m\angle Y = 75^\circ$. Find $m\angle Z$.
$m\angle X = 40^\circ$, so $m\angle Z = 180 - 40 - 75 = 65^\circ$.
$\triangle RST \cong \triangle UVW$, $RS = 3x + 2$ and $UV = 20$. Find $x$.
$3x + 2 = 20$, so $x = 6$.
Ready for more? Take the Unit 5 test.