Fundamentals of Geometry (Leaving Cert Mathematics): Flashcards
📚Flashcards
Practise the cards
15 cards from this deck
ShowHide
Practise the cards
15 cards from this deck
Formal proofs definition
Formal proofs definition
Structured methods proving geometric results using logic
Developer of formal proofs (300 BC)
Developer of formal proofs (300 BC)
Euclid
Axiom definition
Axiom definition
Statement accepted as true without needing proof
Theorem definition
Theorem definition
Statement proven true using axioms and logical reasoning
Four components of every formal proof
Four components of every formal proof
Given, To Prove, Construction, Proof
Theorem 1: Angle opposite longer side is...
Theorem 1: Angle opposite longer side is...
Greater than angle opposite shorter side
Theorem 2: Triangle inequality rule
Theorem 2: Triangle inequality rule
Sum of any two sides third side
Theorem 3: Three parallel lines on transversals
Theorem 3: Three parallel lines on transversals
Equal segments on one = equal on any other
Theorem 4: Line parallel to triangle side divides...
Theorem 4: Line parallel to triangle side divides...
Other two sides in same proportion
Theorem 5: Similar triangles have...
Theorem 5: Similar triangles have...
Proportional corresponding sides
Theorem 6: Base height in triangle
Theorem 6: Base height in triangle
Product constant regardless of which side is base
Theorem 9: Tangent line to circle is...
Theorem 9: Tangent line to circle is...
Perpendicular to radius at point of contact
Theorem 10: Line from centre to chord...
Theorem 10: Line from centre to chord...
Bisects that chord
Proof by contradiction method
Proof by contradiction method
Assume opposite, show it leads to impossible situation
Three triangle congruence rules
Three triangle congruence rules
SSS, SAS, RHS