Topic 10.2 – Angles,
triangles and congruence
Learning Intention
 Formulate proofs involving congruent triangles and angle properties
(ACMMG243)
 Apply logical reasoning, including the use of congruence and similarity, to proofs
and numerical exercises involving plane shapes (ACMMG244)
Success Criteria
 Define proofs and theorems.
 Identify the difference between a proof and a theorem.
 Understand the concepts that support proofs.
The History of Proofs and Theorems…
Euclid (c. 300BC) was a mathematician who
developed a systematic approach to geometry
which relied on proofs.
What are Proofs and Theorems???
• Proof… is an argument that shows why a statement is true.
• Theorem… is a statement that can be demonstrated to be
true.
• e.g. the robber had stolen the wallet, because he had it in his
hand.
Language and Set Out of Proof and Theorems
 Given - a summary of the information given.
 To prove - a statement that needs to be proven.
 Construction - a description of any additions to the diagram.
 Proof - a sequence of steps that can be justified and form part of a formal
mathematical proof.
Evidence for Geometry Proofs
Angles at a Point
Supplementary Angles
Vertically Opposite Angles
Parallel Lines
Angle Properties of Triangles
Angle Properties of Triangles
Equilateral Triangle
Exterior Angle of a Triangle
Exterior Angle of a Triangle
Congruent Triangles
 Same size and
same shape
(identical in all
respects).
 symbol used
for congruency
is ≅
Congruency Proofs
In each of the
proofs, three
measurements
(Angles or Side
Lengths) must be
shown to be the
same.
Example
Example
Your Turn:-
Check for Success:-
Can you: Define proofs and theorems.
 Identify the difference between a proof and a theorem.
 Understand the concepts that support proofs.