Home > Subjects > Mathematics > Level 1 > 1.6 Geometric reasoning (AS91031) > Subject content > Geometry reasons
- Subject: Mathematics
- AS: 91031
- Level: 1
- Credits: 4
- External
Mathematics 1.6 Apply geometric reasoning in solving problems
Geometry reasons
These geometric properties may be used to calculate the size of angles in geometry problems and then given as the reason for your answer.
The reasons can be shortened and the accepted abbreviations are shown.
Download and print a Word document of reasons and abbreviations.
| Reason | Abbreviation | Link |
|---|---|---|
| Vertically opposite angles are equal | vert opp ∠s | Vertically opposite angles Vertically opposite angles |
| Adjacent angles on a straight line add to 180° | Adj, ∠s on str. line | Angles on a straight line |
| Angles at a point add to 360° | ∠s at pt | Angles Around a Point |
| Angles in a triangle add to 180° | ∠ sum of Δ | The Different Types of Triangle |
| The exterior angle of a triangle equals the sum of the two interior opposite angles | ext ∠ of Δ | Exterior angle of a triangle Angle properties of triangles |
| The base angles of an isosceles triangle are equal | base ∠s isos. Δ | The Different Types of Triangle |
| The angle sum of an isosceles triangle is 180° | ∠ sum isos. Δ | The Different Types of Triangle |
| Each angle in an equilateral triangle is 60° | ∠ in equilat. Δ | The Different Types of Triangle |
| Corresponding angles on parallel lines are equal | corresp ∠s, // lines | Angles made by parallel lines Parallel lines |
| Alternate angles on parallel lines are equal | alt. ∠s, // lines | Parallel lines Angles made by parallel lines |
| Co-interior angles on parallel lines are supplementary (add to 180°) | co-int ∠s, // lines | Parallel lines |
| The interior angles of a polygon add to 180(n - 2)°, where n is the number of sides | int ∠ sum of polygon | Angle properties of polygons Calculating interior and exterior angles of regular polygons |
| The exterior angles of a polygon add to 360 | ext ∠ sum of polygon | Angle properties of polygons Calculating interior and exterior angles of regular polygons |
| Isosceles triangle, equal radii | isos Δ, = radii | |
| Angles of isosceles triangle add to 180° , equal radii | ∠ sum isos Δ, = radii | |
| Base angles of isosceles triangle, equal radii | base ∠s isos Δ, = radii | |
| The angle at the centre is equal to twice the angle at the circumference on the same arc | ∠ at centre | Angle at the centre of a circle |
| Angles on the same arc are equal | ∠s on same arc | Angles in the same segment are equal |
| The angle in a semicircle is a right angle | ∠ in semicircle | Angles involved with circles Angles in a semicircle are 90° |
| Opposite angle of a cyclic quadrilateral are supplementary (add to 180°) | opp ∠s, cyclic quad | Opposite angles in a cyclic quadrilateral add up to 180° Cyclic quadrilaterals |
| The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle | ext ∠, cyclic quad | Scroll to Exterior Angle of a Cyclic Quadrilateral |
| The perpendicular from the centre to the chord bisects the chord | from centre to chord | The perpendicular from the centre to the chord bisects the chord |
| The angle where the radius meets the tangent is 90° | tgt ⊥ rad | The angle between the tangent and the radius is 90° |
| Tangents from a point to a circle are the same length | equal tangents | Tangents from a point outside the circle are equal in length |
