Formulate proofs involving congruent triangles and angle properties (ACMMG243)

LO: To formulate proofs involving congruent triangles.


  • The definition of congruence.

  • Proofs are the reasoning behind statements.


  • That justification of reasoning can be completed using proofs.


  • I can formulate proofs involving congruent triangles and angle properties.

Angle Rules

Alternate Angles – The pairs of angles on opposite sides of the transversal but inside the two parallel lines are called Alternate Interior Angles. They are the same measure.

Corresponding Angles – Corresponding angles are formed when a transversal passes through two lines. The angles that are in the same position in terms of the transversal are called corresponding angles. When the lines are parallel, these pairs of angles are equal in measure.

Co-Interior Angles – When two lines are cut by a third line (transversal) co-interior angles are between the pair of lines on the same side of the transversal. If the lines are parallel the co-interior angles are supplementary (add up to 180 degrees).

Triangle Congruency Rules

RHS (Right-angled Triangles) – Right, Hypotenuse, Side

SSS – Side, Side, Side Congruence

SAS – Side, Angle, Side

AAS – Angle, Angle, Side


When figures are similar, they have the same shape and proportions. When figures are congruent, they have the exact same shape and size.

One common mistake is that ‘AAA’ is NOT a congruency rule. Triangles can have the same three angle measures, but it does not mean that the triangles are congruent.

Proof Videos

Passy World
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