Congruent triangles

Topic outline

• Outcomes

  Collapse all Expand all

  
  

  In this course you will learn about:

  1. Conditions for congruency.
  2. Proving congruent triangles.

• What does congruent mean?
  If two triangles are congruent, then they are identical in every way. In other words, congruent triangles have the same size and shape.

  • Mark as done

    Visualising congruent triangles

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

    
  • Mark as done

    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. 

    
    

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

  • 

    Name the equal angles and sides Quiz

    Mark as done
  • Mark as done

    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.

• Proving triangles are congruent

  To prove that triangles are congruent you must show that they satisfy one of the conditions for congruency. Your proof of congruency must contain three statements with reasons to show that the triangles are congruent. There is a specific way that the proof of congruency must be set up, this is discussed in the video lesson that follows. 

  • Mark as done

    Setting up the proof for congruent triangles

    In the next video you will use geometric properties to prove that triangles are congruent. It is important to follow the steps carefully to set up the proof for congruency. 

  • Mark as done

    Practise: Prove that triangles are congruent

    Follow the link to the exercise Prove triangle congruence to test that you understand how to write a proof with statement and reason for congruency.

  • 

    Attribution & licence Page

    Mark as done