Sectieoverzicht

  • If two triangles are congruent, then they are identical in every way. In other words, congruent triangles have the same size and shape.
    • Leerlingen moeten
      Als voltooid aanduiden

      Visualising congruent triangles

      The animation here shows how congruent triangles can be translated and rotated to give the same figure.

      Congruence en
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      Als voltooid aanduiden

      Symbols and notation used

      The symbol \( \equiv\) or \(\simeq \) is used to show that shapes are congruent. 

      If two triangles are congruent, then each side in the one triangle will be equal to each corresponding side in the second triangle. Also, each angle in the one triangle will be equal to each corresponding angle in the second triangle. 

      The order of the letters when stating that two triangles are congruent is very important. The letters of the corresponding vertices between the two triangles must appear in the same position in the notation. For example, in the diagram \( \Delta ABC \equiv \Delta DEF \) because it indicates that \(\angle A=\angle D, \angle B=\angle E, \angle C=\angle F\) and AB=DE, BC=EF and AC=DF. 

      triangle ABC drawn congruent to triangle DEF

      Try the next quiz to check that you understand how to name congruent triangles correctly.

    • Name the equal angles and sides Test
      Leerlingen moeten
      Als voltooid aanduiden
    • Leerlingen moeten
      Als voltooid aanduiden

      Conditions for congruency 

      There are four ways to prove that triangles are congruent:

      1. \(SSS\) (all corresponding sides are equal)
      2. \(SAS\) (two corresponding sides and the angle between those sides are equal)
      3. \(AAS\) (two corresponding angles and any corresponding side are equal)
      4. \(RHS\) (both triangles have a 90°angle, equal hypotenuses and one other side equal).

      Watch the next video to learn how to identify congruent triangles.