Geometry / Unit 5: Congruent Triangles
5.3 SSS and SAS Congruence
Notes
You don't need all six pairs of parts to prove triangles congruent.
- SSS: three pairs of congruent sides.
- SAS: two pairs of congruent sides and the included angle (the angle between those sides).
- A shared side is congruent to itself (Reflexive Property).
- Example: in $\triangle ABC$ and $\triangle DEF$, $AB = DE$, $m\angle B = m\angle E$, $BC = EF$. The triangles are congruent by SAS.
Practice
$\triangle ABC$ and $\triangle DEF$ have $AB = DE = 5$, $BC = EF = 7$ and $AC = DF = 9$. Which postulate proves them congruent?
All three pairs of sides are congruent.
$\triangle PQR$ and $\triangle STU$ have $PQ = ST$, $QR = TU$ and $\angle Q \cong \angle T$. Which postulate applies?
$\angle Q$ is between sides $\overline{PQ}$ and $\overline{QR}$, so it is the included angle.
Quadrilateral $ABCD$ has $AB = CD$ and $BC = DA$. Diagonal $\overline{AC}$ splits it into $\triangle ABC$ and $\triangle CDA$. Why are these triangles congruent?
Two pairs of sides are given and the shared side gives the third pair.
Ready for more? Take the Unit 5 test.