Luca Truen Gr11 Mathematics Page 1 of 3
Euclidean Geometry
Terminology
- Arc: a portion of the circumference of a diameter is the length of a straight
circle. line segment from one point on the
circumference to another point on the
- Chord: a straight line joining the ends circumference, that passes through the
of an arc. centre of the circle.
- Radius (r): any straight line from the - Segment: A segment is a part of the
centre of the circle to a point on the circle that is cut off by a chord. A chord
circumference divides a circle into two segments.
- Diameter: a special chord that passes - Tangent: a straight line that makes
through the centre of the circle. A contact with a circle at only one point
on the circumference.
Axioms
An accepted principle
1. The theorem of Pythagoras states that the square of the hypotenuse of a right-
angled triangle is equal to the sum of the squares of the other two sides.
(AC )2 = (A B)2 + (BC )2
2. A tangent is perpendicular to the radius drawn at the point of contact with the circle
Theorems
Formal proof of a geometric fact
Perpendicular line from circle centre bisects chord
Statement: If a line is drawn from the centre of a circle
perpendicular to a chord, then it bisects the chord.
Reason: ⊥ from centre bisects chord
1.Construct radii
2.Theorem of Pythagoras to prove chord is bisected
Euclidean Geometry
Terminology
- Arc: a portion of the circumference of a diameter is the length of a straight
circle. line segment from one point on the
circumference to another point on the
- Chord: a straight line joining the ends circumference, that passes through the
of an arc. centre of the circle.
- Radius (r): any straight line from the - Segment: A segment is a part of the
centre of the circle to a point on the circle that is cut off by a chord. A chord
circumference divides a circle into two segments.
- Diameter: a special chord that passes - Tangent: a straight line that makes
through the centre of the circle. A contact with a circle at only one point
on the circumference.
Axioms
An accepted principle
1. The theorem of Pythagoras states that the square of the hypotenuse of a right-
angled triangle is equal to the sum of the squares of the other two sides.
(AC )2 = (A B)2 + (BC )2
2. A tangent is perpendicular to the radius drawn at the point of contact with the circle
Theorems
Formal proof of a geometric fact
Perpendicular line from circle centre bisects chord
Statement: If a line is drawn from the centre of a circle
perpendicular to a chord, then it bisects the chord.
Reason: ⊥ from centre bisects chord
1.Construct radii
2.Theorem of Pythagoras to prove chord is bisected
