- The triangles shown are ΔPON and ΔLOM.
- The tick marks on sides PN and LM indicate that these sides are congruent: PN ≅ LM.
- The angles at vertex O, ∠PON and ∠LOM, are vertical angles. Vertical angles are always congruent, so ∠PON ≅ ∠LOM.
- The tick marks on sides PO and LO indicate that these sides are congruent: PO ≅ LO.
- We have two pairs of congruent sides (PN ≅ LM and PO ≅ LO) and the included angle between them (∠PON ≅ ∠LOM) is also congruent.
- By the Side-Angle-Side (SAS) congruence postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
- Therefore, ΔPON ≅ ΔLOM by SAS.
Parent Tip: Review the logic above to help your child master the concept of triangle congruence asa aas and hl worksheet answers.
