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2.5 – Proofs of Congruence

Objectives

  • Explore congruent triangles using the shortcut postulates (SSS, SAS, and ASA), the AAS Theorem, and CPCTC.
  • Use Thales’ method and triangle congruence shortcuts to measure the distance of enemy warships from the shore.

 

No Key Terms

 

Notes

Congruence Reasoning
Geo A 2.5 - Congruence 01
Proofs
  • Proof: Vertical Angles
    • What do I want to prove?
    • What do I know? (What is given?)

Geo-A-2.5-SAS-CPCTC

  • Proof: Isosceles SSS
    • What do I want to prove?
    • What do I know? (What is given?)

Geo A 2.5 - Congruence 02

Geo A 2.5 - SSS Proof
  • Proof: Parallel Lines & Triangles
    • What do I want to prove?
    • What do I know? (What is given?)
  • Remember
    • Theorem: When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
      • \overline{MN}\parallel\overline{QP}
      • \overline{MP} is the transversal
      • \angle{NMP} and \angle{QPM} are the two alternate interior angles
    • Converse (True in Congruence Proofs): If two lines are cut by a transversal so that alternate interior angles are congruent, then the two lines are parallel.

Geo A 2.5 - Skew Triangles

  •  Proof: Reflexive Property (Reflection) with ASA
    • What do I want to prove?
    • What do I know? (What is given?)

Geo A 2.5 - ASA

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